My synopsis of the situation you are in:
* You are short of fuel - 1500 fuel a day at Truk will seriously undermine you ability to move the big fleet you have (or will soon have) around.
* You are short of supplies - 2000 a day to run the bases. It is nice to have 20000 at Rabaul to enable replacements of lost aircraft, but it is also imperitive to have a bit of a stockpile in the more forward bases. You will struggle to get supplies forward so you need to get them there early. This is incongruous with the amount of supplies you receive and the allied ability to interdict your resupply efforts. There are about 9000 supplies sitting on the island SE of Truk, with no job to do, seriously recommend you go and get them.
* You have no shipyard in the game area. So you cannot repair major damage and sending the ships back to Japan is tantamount to taking them out of the game (due to return times). You'll have to consider whether you keep damaged ships around or if the damage is too great that it is safer to send them home.
* You have an initial spurt of warships, such that you will actually outnumber the allies. The difficulty you have is using this advantage because -
* you are outnumbered by allied CV airpower. If your opponent has constructed his CV TFs around single CVs then it is going to be very difficult to get a decisive carrier victory. Unfortunately, this is what you need in order to bring your early superiority in surface warships numbers to bear. If he can sit back under an umbrella of CV air this superiority is moot. As FatR has already stated, you therefore must attempt to engineer a battle in which you can use your land based naval ACs to offset this numbers deficiency. A perfect outcome is to have a two+ day battle in which the first day is taken up by your LBA against his carriers, where you manage to get a strike on one or more of his carriers, then a second day of your carrier based air against his carriers.
* the victory point allocation to bases is heavily biased to 3 bases: Lunga, Port Moresby and to a much lesser extent: Milne Bay. In order to win the points game you have to take one of the first two and hopefully also Milne Bay. Saying this is hard really is being euphemistic. Personnally I think it is more possible to take Port Moresby, especially if you actively interdict reinforcement TFs before your invasion. But holding on to it is another thing entirely. You cannot stop Lunga being taken, and it is taken by the marines. They are tough customers and your lift capacity makes it difficult to get enough troops there, in one lift, to engineer a victory.
* With no shipyard you get no ship upgrades. Not so your opponent, and you will really notice the differences, especially with destroyers. They are already very hard to hit with Naval ACs, but when they get the 5" naval gun upgrades and radars they can foot it with your warships and cause damage out of proportion to their value, because they hit so often now. You'll be reticent to go into surface combat. Allied subs will get their better torpedos, and because of their number and your relatively poor ability to destroy them, suddenly all the choke points/areas are very dangerous for your high value capital ships.
* you have enough transport ability to mount a medium amphibious invasion. But these same transport ships have to try and keep the forward bases in supply. This will be your hardest task. Any large loss of transport ships (an enemy surface group gets amongst them and wipes them out), and you're in serious trouble. Because his subs and planes will keep nibbling away at your transport numbers as the game goes on, and those forward bases will be harder and harder to resuppy.
* However, you do have the ability to use warships to carry supplies (fast transport TF). You'll use them alot for this as it'll get awful hard to get the supplies in using AKs etc. Trouble is, you also need these ships being warships... The initial mass of numbers quickly starts to look inadequate once losses start to accummulate and the jobs you need them to do go up in number.
* Allied heavy bombers are unstoppable. Be very very careful about using Rabaul's port for repairing ships. He can hit Rabaul from Oz, so taking PM is not a way to halt this. If he holds PM, he can even hit Truk with some variants of the B-24. If ship repair wasn't hard enough before, this allied ability makes it even more fraught with danger.
So, having bored you to tears with stuff you probably already knew about with the scenario. Lets look at how I think you should approach things:
In order to win the points game you must take AND HOLD (until the end of the game - and there's the rub), either Lunga or PM. Since Lunga will be taken by the marines I chose PM in my PBEM. The problem with PM isn't so much the taking but the holding. It is so close to Oz that he can have strong forces on you, and keep them there, much easier than you can defend the place. In other words, it is a prime location for both sides to invade.
In order to take either you'll have to bring some serious ground forces. If you chose Lunga I think I'd recommend doing it in two hops. Bring the troops you need forward to Rabaul, then invade from there with the ability to go back to Rabaul and bring more troops (rather than all the way back to Truk).
You have to either take out the allied CVs or time things superbly such that he is refuelling and rearming just when you are landing. Even then, it is VERY likely he will do his best to interdict your effort with the carriers. Honestly I think hoping for this scenario is wishful thinking. I don't think you have time to do an invasion without coming to grips with his carriers.
So, lets assume you do have a go at the carriers.
You have to somehow bring the odds down. To do this I would recommend either the option put to you earlier: 2 days of combat with LBA hitting him first, taking whatever you can get. Another option is to round up as many zeros as you can find and defending a TF of destroyers that you purposefuly put in range of his carrier air. You are after attrition and damage of his strike groups. Then hit him the following day, making sure your carrier TFs have BBs in their midst and other targets for him to hit. Get those opposition numbers down. And set your carrier groups up to have about 20% CAP 80% escort. You have to get the strike package to the targets, so at least escort them.
Assumming you manage to pull of a reverse Midway or at very least sacrifice your carriers taking his down too, now you have the surface might to own the seas in the danger zones.
Recon your targets well (so that bombing and bombardment raids do the most damage), use your BBs to bombard and well led surface combat groups made around your heavy cruisers to protect the invasion. Remember that your BBs are likely to have to retire to Truk to rearm (unless you can get some naval support to Rabaul). If you have chosen PM to invade you are still able to put air defence over the invasion, at Lunga you'll have no such luxury unless you've managed to build up one of the Solomons islands, unfortunately this is difficult because all of the islands are zero rated air strips and getting them to level 1 could just take too long. Another reason why I targeted PM.
Having pulled all these things off, without adequate supplies or fuel, you'll now be landing more troops than he can defend against and will take your target. Now you have to hold it.
This is the really difficult part.
Heavy bombers, functioning allied sub torpedos and upgraded allied destroyers making keeping a target in supply very tough. When you can't stop the heavy bombers, and supply hits taking a percentage of the supplies at a base, just loading a place with 100k supplies (actually an impossibility with this scenario, but you get the idea), will also not work as each hit will take proportionally more supplies. The only answer is frequent re-supply efforts. Holding PM I found Buna invaluable - offloading the supplies there and manipulating the supply request at PM, pulling the supplies across the mountains.
Lunga does have the benefit of being a bit more isolated. But if he loses Lunga he is almost certain to build Efate Port Villa, and doing so will make resupply of Lunga just as hard as PM, and there is no nice port like Buna with a land bridge to move your supplies from at Lunga (although there is Tassafaronga but it is as vulnerable as Lunga itself). These land-bridge locations become even more important when you lose air or naval superiority, as you almost certainly will. Because he will simply park naval units at your base and dare you to come and flush them out. Now you are fighting on his terms and with dwindling power. However, if you don't offer battle you can't resupply... tough problems to find solutions for.
The later part of the game is about hanging in there until the clock winds down. Getting those supplies in to whichever location you've decided to hold, is vital. The allies will have better weapons and more of them than you in every arena other than army/land units. Your land units are still very very good, unfortunately they don't go so well without food or bullets. Get some naval support forward too. They will help immeasurably in getting the supplies off the ships. This especially helps with fast transport missions. They want to be in, unloaded, and out by morning. If you don't have enough naval support at a base then they will still be unloading in the morning and that has obvious consequences.
You've chosen a very tough assignment for your first PBEM. But if you do manage to gain a draw or minor defeat/victory other than an allied decisive victory, you'll deserve a pat on the back. Don't lose faith in the game over this one scenario is all I'd say.
Image courtesy of Divepac