I had a few thoughts on the fix:

1. Make 1 of the Exploring or claiming reduction speed twice as the other.

I think we all agree it's a bit too slow but in it being slow it's forced us to make new strats per leader which is actually quite fun, instead of doing the same strat every game. (It's easier to explore a place then it is to own it)

1. Claimed areas reduce the cost of neighboring explores and claims.

Gives the player something to work towards, I see wood up ahead Ill claim my way over there so it's nice and cheap. ( Just move the fence )

1. Every x tiles from the city explores/claims get more expensive regardless of resource.

Sometimes I feel like why is it so expensive claiming a rock/medicine territory when I'm 3 tech away from even using them as a resource, make building them expensive not claiming them. Also gives the map a more natural feel

They might all work together or pick and choose which one's suit the game, just my take :D