First off, a strategic bomber is imo a must in any setup. They work wonders, and when you are up against naval targets, even more so.
1. Use strategic bombers on Cruisers and Battleships, use your own cruisers and battleships on enemy destroyers, send your subs against capitol ships only, and use your destroyers against weakened enemy destroyers only. Remember that the Bf109 can usually deal with a 1 strength enemy destoyer as well.
2. Try to get the paratroopers to the north. This might require you to keep them somewhat back for a turn or two.
3. Go after enemy fighters that are not protected by AA units whenever possible, and it is better to destroy 1 enemy unit than to cripple 2.
As to your prestige issues;
-if you are near the end of the scenario, do not rebuild a unit, keep it back and below strength untill the scn is over, as rebuilding is alot cheaper in the deployment phase.
-are you upgrading your panzers in a non efficient way? The various PzIIIs can upgrade into eachother rather cheap, same with the versions of PzIVs. I try to keep two separate lines of tanks, one anti tank (PzIII then eventually Panther), and one anti soft (Pz IV then Tigers). I never change a PzIII to a PzIV or the other way around, this saves alot of prestige. The same goes for Aircrafts. Changing between the various types of Stukas is cheap, changing a Stuka to a Bf110 is not. Also the case with artillery if I do not recall incorrectly.
Not buying units;
that is a big no no for me, I always buy the units possible, even if it means that I need to start a unit off as a PzI just to be able to afford it.
You do not list what your unit list looks like, that would be a great input as it helps show what might be draining you on prestige. Usually for me around Sealion, the list is something like this (taken by memory so might be a little off)
-3 or 4 fighters
-2 or 3 Tactical bombers (I never buy new Bf110s!!)
-1 Strategic bomber
-4-5 Infantry (pioneers all except those I have been awarded, which are changed to HW)
-6 tanks (3xPzIII, 3xPzIV)
-1 TD (these guys are invaluable later on, but for now 1 is enough since they are not good enough just yet, but buy another one later one).
-2-3 arty. Towed ones.
"Hun skal torpederes!" - Birger Eriksen
("She is to be torpedoed!")