One of my oldies, Polly, keeps waking me up with insistent little 'wew' sounds. Doesn't bother me though, as I can catch up in the day (she does it then too, think she hates me being asleep!)
So, what's a little lost sleep? That's my attitude, but I don't work (disability).
Try taking your cat back to the vet for tests he/she may not have originally carried out.
Is there any particular trigger, or pattern to your cat's crying. Does it only happen in the dark? (Try a nightlight.) Or when it's very quiet (leave a quiet radio/telly on downstairs). Or when your cat feels lonely (the telly may help with this, just quietly).
Ignore the bloomin neighbours, your cat is more important.
Personally, I wouldn't consider rehoming or pts unless THE CAT is suffering. You'll forever feel guilty if you do it for your convenience (don't mean that harshly).