The simplest solution would be to remove the 'system wide training' abilities as Psychic only bonuses. That is, make all training facilities system wide.
Would that be considered a hit for the value of the Psychic trait?
A better sceheme for SE V would be to change the way experience works. I emailed MM with a new system a while ago but I dunno if he's working on SE V yet.
The current system is a bit crude. When you need to build larger ships you cannot carry over your experienced crews to the new ships, for example. Someone suggested in another thread that we should be able to 'transfer' crews to new ships when we scrap old ones. Keeping track of 'crews' is a bit difficult since a 'crew' is actually a composite of hundreds or possibly thousands of people/creatures. And the number of crew required for each given size/class of ship is going to be different, not to mention differences caused by changes of the equipment in use. An 'experienced' crew of a missile ship is not going to be nearly so competent if you transfer them to a carrier. How do you track the 'type' of training that the crew has? And anyway, the AI cannot use the current system effectively. How would it handle a more complex system?
I think that what is required is some sort of 'pool' of crew experience based on the number of ships in you have in service and how long they are in service. A sort of 'accumulated hours of operation' measurement, averaged over the number of ships you have. As this pool grows larger relative to fleet size, the default experience of your ships can increase because you can assume a better general level of training in your 'armed forces'. But ships getting destroyed in combat means dead crew, so you should also suffer losses from your pool due to losses of ships in combat. Ship and fleet training facilities will still have a use, but they should just add to the global 'experience pool' so that it will increase even if ships are not earning experience in actual combat, or recover faster from losses. This would be much more usable by the AI than the current system because you wouldn't have to park your ships in a special location for a certain amount of time.
Ships should still gain experience individually for success in combat, but then their new experience would be 'average in' to the general pool. Most individual ships would just rely on the empire-wide 'average' experience/training level. This would tend to 'even out' the differences between ships and make most of your fleet have a similar level of effectiveness. I suppose some people will not like this feature of the system. But isn't that how it works in real life? Do navies in our world generally have radically different levels of crew competence among their ships? Don't crew members actually get shuffled among ships quite a bit? You shouldn't take Star Trek for an accurate portrayal of military service. It's actually quite rare for one officer to stay with one ship for 5 years or more. If you still want to have 'elite' units than maybe you should be able to give some of your ships a special designation as 'elite' and pay extra maintenance costs for their extra training so they can be above the fleet average.
Yes, this would eliminate the usefullness of the 'reassign crew' intel project. But this type of system would be so much more realistic. It would effectively make trained crews a 'resource' that you would have to develop and manage, and could lose in a disastrous war. Managing the 'man power' (creature power?) of your armed forces in this way would be simpler (no parking ships over training facilities and checking to see when they're 'ready') than the current system, and yet more fun.