Actually I see another possibility that might work for everyone, since it doesn't involve removal of fixed borders. How about if you have fixed borders, then cultural pressure against you operates by (significantly) increasing the local rebelliousness in the culturally over-powered cities. That way the fixed borders would continue to operate as now (so cultrure wouldn't slowly win you tiles), but full on rebellions (and city flips?) would start to occur to the player who is being culturally overpowered.
I haven't looked at the code at all yet - just throwing this out as a mechanic we could explore...
I would love this implementation.