Sounds like he may have lasting damage from those UTI's.
You could perhaps try putting puppy pads on all his favourite sleeping spaces? Cats love sitting on things, so he'll probably go straight for them too.
Those things are super absorbent. I use to them to line crates & carriers whenever I fly with my pets.
There are also supplements you can use to help strengthen the urinary tract, but you may want to consult a vet that you trust to find one that will work for your cat.
Stuff like this http://www.nativeremedies.com/petalive/products/better-bladder-control-leaking-urine.html#tabset
Also! Adding a fish oil/seal oil might be beneficial - it helps with reducing inflammation as well as other things, and will help to ward of infections.
I also think another vet trip may be warranted, as dribbling can sometimes be a warning sign of a mild UTI forming again, though it could just be lasting damage. (Which is honestly what it sounds like, but ya know, cover all the bases.)