Impossible further progress on problem of PhD thesis
This sounds very familiar. Concrete advice in this situation: Focus on writing the paper.

You have some contribution, new arguments as to why the general problem is hard, progress on parts of the general problem. This really sounds like a possible paper - so write it and, if discussed with your advisor, submit it to the right journal.

Postpone your decision on further steps to this point. The situation may have changed completely until then - and if not, you will still be much better prepared to discuss the matter and to decide.

(Caveat: It may also happen, that, during writing, you'll find new ways to attack a more general version or find flaws/gaps in your current reasoning… anyway, writing the paper also help with this.)