A) Get screenshots of the fights. Preferably several ones (like, per fight-hour), with you mousing over some of the ships in the fight so we can see the modifiers.
B) don't put CV's in your transport fleets; Xports slow the fleet's average speed SO far down that even older SAGs can close the distance and start pounding everything... including those carriers.
C) Put your Older Capital Ships as X-port escorts. type I/II BBs or BCs, CAs... those ships are good for not much BESIDES escorting transports (their slow speed won't let them catch up to ships they actually want to shoot at... but if enemy fleets are attacking YOU, they will get a chance to do what they do). If you are JAP, then the Yamato and Musashi, post-1941, are IDEAL for this role. My favorite "transport" fleet is DBB Yamato, DBB Musashi, and 10 transports.
D) While you dont want to mix CV and SAG fleets, you CAN put them in the same seazone; the result will be that the SAG fleets move to engage, the CV fleets hang back. This will provide aircover, as the CV's CAGs will "CAG duty" the attacking ships WHILE your X-port's SAG escorts are exchanging fire.
E) Always haev your transport fleets have 50% more transports than you need for an invasion. As in, if you need 3 transports to carry your force, don't leave with less than 5; nothing's worse than having 1/3 of your landing force straight up die due to a lucky hit.
F) Kee an eye on your health. Even if your invasion is going well, if you notice your ships are starting to fall, order a retreat. Sea-battle retreats take several hours to "work", but they still do.