I'm so sorry to hear about the stomatitis! But, before we get too far ahead of ourselves, is it definitely stomatitis? I've learned that many vets umbrella any and all oral inflammation under "stomatitis", which is very inaccurate. And, it is VERY important to have an accurate diagnosis, as the treatment for TRUE stomatitis is very different from the treatment of other oral diseases.
The hallmark of true stomatitis is that the inflammation extends past the gumline and into the throat and/or cheeks. Unfortunately, true stomatitis is not treated with a basic dental. Rather, significant extractions are required - either full-mouth ("FME" - every single tooth, which is what my kitty had - and she is thriving!), or partial-mouth ("PME" - everything behind the canines). The type of extractions (FME vs PME) depends on the extent of the disease, and it is best to let the vet/dentist determine which is the best approach after they do an under-anesthesia exam on the day of the surgery. It is absolutely vital that the vet/dentist take x-rays both before and after the extractions; if ANY root/tooth material is left behind at all, it will continue to cause problems.
However, if he just has gingivitis and not actual stomatitis, then a traditional cleaning with extractions of only bad teeth is what you want to do (I would still insist on before and after x-rays).
Since the treatment is so drastically different, it is very important to have an accurate diagnosis. Personally, I would suggest seeking out a veterinary dentist if possible. Stomatitis surgery is definitely different from "every day" extractions, so you want someone with a lot of experience and knowledge. Treating the dental problems could very well help with his BGs!
As Wendy mentioned, there is a pretty good FaceBook group for stomatitis...but if I'm being honest, like many other FaceBook groups, you do get bombarded with some extreme opinions, so that is something to be prepared for. I found the group to be helpful, but I also spent a lot of time doing my own research as well.
I know Shooter is diabetic, but I actually wonder if his ravenous appetite and excessive thirst could be from hyperthyroid. It is worth investigating - FD and HyperT do share a number of symptoms. It's important to note that there is a "gray zone" in the HyperT test range, where the total T4 is high-normal, but kitty has symptoms. If this is the case, you want to run a Free T4 to rule Hyper T in or out. On the good side, if he does have HyperT on top of other things, it is usually pretty easy to treat.
Please let me know if you have any questions or need any further help/guidance. Prayers for your boy!