A couple of observations...
Vets like to prescribe Convenia because it is a long acting antibiotic and you don't have to pill your cat. However, the only pharmaceutical indication for its use is for skin infections. It's not a good antibiotic for a UTI. What they should be doing is a cystocentesis (inserting a needle into your cat's bladder to get a sterile urine sample) and then the urine sample is cultured in order to figure out what the bacteria is so the appropriate antibiotic can be prescribed. (It's called a "culture and sensitivity). Given you've been having limited success with what's been prescribed, the vet should know this. Your regular vet should also know how to do a cystocentesis and culture and sensitivity.
The UTI is likely the cause of the high blood glucose numbers. Any infection or inflammation will cause those numbers to be elevated.
Unless you have a veterinary endocrinologist in your area, it's unlikely that you'll find a vet that specializes in diabetes. What I would suggest is looking for a feline specialty clinic. There's a
cat only practice in Allentown. The alternative would be to find an internal medicine specialist. You may need to go to Philadelphia/University of Pennsylvania vet clinic if you want an internal medicine vet, though. You could also check with Penn's vet clinic to see if they have any locations outside of Philadelphia.
It may take more than an hour for a Prozinc dose to kick in. Onset (when insulin starts to work) is often more than an hour especially since you're feeding your cat at around the same time. Also, 345 and 355 are pretty much the same numbers. There's up to a 20% variability in any test.
Wendy and I have been members of FDMB for a long time. I haven't a clue what a "typical" diabetic cat is. If I had to place a bet, I would suspect that your local vet has limited experience with treating feline diabetes. The folks here have lots of experience! This website has been around for 25 years. If you want to get started here, we recommend that new members create a spreadsheet and signature. The information is in this post on
helping us to help you. The spreadsheet will allow you to keep track of Cookie's progress and will allow us to follow along. The signature has basic information about your cat so we don't keep bugging you with the same questions.