Making starbases movable was easy, and works fine for actual human playerse, but the AI still refuses to move their own starbases. Not sure what I'm overlooking (I hope it's something simple). Is it still something within the entity files, or is it a whole different can of worms?

All I did was modify the PSI and TEC entity files for starbases.  I assumed that setting the default spawn of each starbase to "Gravity Well" instead of "Hold Position" tactical setting would make them move them, but apparently not.  It works for players (my starbases move automatically to defend), but the enemy AI's just sit there like a giant lump of space potatoes.