For EUBanana, you can send pilots from squadrons to the general reserve, from where the other squadrons in the same nation can pull them. Sadly, as the USMC and USN are considered different nations you can't use USMC squadrons to train carrier pilots

The pilot transfer process goes like this. Open the squadron pilot screen and hover your cursor over their name, the popup will tell you which click does what. There is a difference because you can send high-exp pilots to tracom while you can't do it with low exp ones. Use the click which sends them to general reserve.
Now go to the other squadron that needs pilot replacements and click on the "request veteran" option. A list of pilots should appear, with some of them assigned to the previous squadron. Click on the pilots you want to bring to the new squadron and they should arrive in a number of days indicated by the delay column.
Now there is a catch, they won't become active automatically. When the delay reaches 1 you need to activate them yourself through the pilot screen. If you don't they will dissapear to somewhere after a while (a week? A day? I don't know atm).
Where they dissapear I do not know, perhaps they will come back in 180 days, perhaps they dissapear forever, I have no idea, I haven't been able to figure that one out yet. I lost about 20-30 good pilots that way before I finally found out about that "feature" .
This feature is rich in micromanagement but it's a great way to really get the good pilots into the squadrons you want them in. If you wish you could just create an all out "ace" squadron from one of your early F4U units and use it to utterly devastate the japanese. Or well, whatever you wish.
Now using the training command won't give your pilots high exp, doing real missions will. High exp, however, will reduce the fatigue the pilots take as well as ops losses and various other small things that aren't covered by the specific skills. Basically you also want high exp in addition to the high skill for your front line units, especially carrier units.
Now the Japanese have a nice advantage here. Recon and transport units, especially the latter. Just flying supply missions and recon will gradually increase your general experience level the way that usual training never will. After they have high exp transfer them to the other training squadrons and train them in the skill they need, then transfer them to the frontline. It takes more time (as it should) but will provide true top notch pilots.
The USN might be able to do the same if there are any USN transport or recon units available. IF there aren't you could just use pilots from PBY squadrons, flying extensive naval search should also up the exp levels. Sadly you're also going to need all the good PBY pilots you can get.