Early game, I don't mind the varied starts, it makes every game different, I don't need the exact same balance each time.
Mid game, I agree to an extent to help races from running away too much, especially very productive ones.
Minor races will help slow this, I hope, claiming a planet and possibly a system for themselves. If you settle in their system I hope they drive you out of it, at least till later game. Give minor races some nice defensive ships, but poor offensive is how i'd do it, with perhaps military starbases backing them up.
UP could vote on this to make colonies more expensive mid game. Either races falling behind might agree(to stop anyone falling further), or races way out in front might agree (to stop anyone catching up), so it'd be down to personal player preference on when to vote. The AI could use the tech age as a base for it's vote, or how many planets are left in the galaxy, or it's size relation to its neighbors in the early game, or if its currently in too many wars to colonize so it'd rather slow everyone down. You could also do it via ideology, the cost be associated with making colonists lives more comfortable.
Better enemy AI not liking you colonizing right on its borders, it should warn you about this directly, especially the expansionist type races, Dregin, or Human not to come too close.
More AI players will help with this, as essentially you'll have settled all there is peacefully to settle, unless we get to use the dead planets for outposts or some such. I hope some mechanic uses them in the end, pirates, minor races or mercenary groups etc.
Neutral zones could be established diplomatically in the UP or between individual races, to allow room between races.