A new strategy idea is a much tougher challenge, though. And I was hoping to think of something that would reduce the micro to the point where I wouldn't absolutely feel too lazy to join the fray. :-)
Max micro explorers is so powerful. It gives you such a nice competitive advantage. Tech bonus from wrecks, planet squishers, ruin techs, WotA, knowledge of resource rich clusters, super luxuries, clusters of habitable planets, indies. That big and scary unknown void can turn into a lunchbox pretty quickly, but on the other hand it's a micro nightmare of the worst kind to carry out the approach on a 1000+ system galaxy. Without some sort of limitation on how effectively you explore the universe, the optimal approach will necessarily involve a frankly rather silly amount of time invested into making sure every scout is operating at peak capacity. Making your explorerers dumb is one way to do it. Making them numerically limited is another.
However, if you don't want to hold yourself back like that then how about respawning pirates? They're not strong enough to really screw you over, but they're strong enough that you have to be more conservative with your defense and since they respawn, you can't just send out a fleet to clear an area permanently.
Alternatively, how about a bit of roleplay? No sneak attacking while at WotA, no declaring wars of convenience while using a "peaceful" race or government type? Maybe even try to follow the tech priorities specified in the policy file of your race of choice? Granted, this is still more of a personal limitation than an actual strategic paradigm change, but it's hard to change the strategy much as long as the objective is to win as massively as possible with no holds barred (beyond early derelict capital ships and tech trading), since most games really do reward one approach at least a little bit more.
Anyway, the above was me offloading some stray thoughts on how to get a different experience by changing the context, which is something we can probably achieve even more efficiently once Universe arrives. I suppose the relevance is somewhat questionable, even if I felt like writing it all the same. You're asking for strategy ideas for the current context? Well, you might gain a tiny bit by obsoleting civ ships during the early pre-ward research era. There's no point in wasting resources on what is by and large a cross between pirate bait and floating space debris with directional thrusters.
I'm sure there's some potential for space port location optimization but it's a pain in the ass to figure out exactly how to do this optimally. I tend to think less is more in terms of the number of space ports but then I'm also new, inexperienced, and for some reason most of the "older" people around here seem to think differently.
For research, I think the proper order of things is more or less well established. For energy, the priority is proper warp drives, shields, ranged resource scanners, and long range scanners. Then better reactors, warp drives, and engines that can actually move bigger hulls. For weapons, the priority is reasonable troops, armor for your ships, and then ultimate torpedos. Point defense, logistics, ion defense, and of course mech infantry are probably next. For HT, the priority is getting energy collectors, biggers hulls, wonders for some fairly massive competitive advantages, maybe the early colonization techs, and then better cargo bays, fuel cells, docking bays, life support systems, in roughly whatever order you feel like. Targeting systems, ECM, and damage control are also quite nifty research targets at this point.
Some variation of the above approach gives you what you really need as fast as possible, doesn't it? But one thing that does spring to mind, and which I haven't seen anyone mention, is that once you've got those weapon basics, you don't really seem to need more weapon research for a while, do you? Would it be worth it to downscale your weapon research, shifting the majority of your research points to an even split between energy and HT? Going from 33% to 50% of your imperial potential research is essentially a 50% increase and it seems to me that a hyperfusion reactor, good engines, and size 700+ hulls are more beneficial than having the option to put laser weapons or area weapons onto your ships.
What else is there? Getting as much utility as possible out of mining stations and civilian ships? I'm sure you're doing that already. Long range scanners and science labs on stations? Why not? Using gas mining stations as strategic resupply depots with an appropriate docking and cargo capacity? Again, why not? It's not like the civs have a hard time paying for it. But I'm pretty sure you're the one who inspired me to throw science labs on mining stations in the first place so I'm sure you're already doing your best to push as many of your expenses onto the private sector as possible.