Oh Hannah
I don't know what to suggest. Part of me thinks I'd shut him in the bathroom overnight (guessing no wallpaper in bathroom) so if he wees it's on a wipe clean surface rather than beds and carpets but I fully understand your worry about stressing him further.
Is there any way you'd be abe to get a urine sample from him? Just thinking it might be worth taking a sample into the vets just so they can check if there's any trace of infection. Is it proper big wees he's doing around the house or more 'dribbly' amounts? Is he weeing in his litter tray at all?
I can't remember if Jasper goes outside or not but is it possible that a new cat has moved into the area and he feels his territory is threatened either by having smelt that it's been in his garden when he's been outside or having seen it through the window and that's what has stressed him?
Pinball said he'd like to send a wimpy hug and a squeak to Jasper and hopes he cheers up soon xxx