I'm not sure that I agree with your vet about the gum inflammation being responsible for these high numbers. Infection and inflammation definitely can increase blood sugar, but to my eyes - and this is simply my opinion - the issue is that the Lantus dose was started too low. I would be asking if the inflammation only occurred after you reduced the dose?
There are many reasons cats might need more than 2u of insulin. Appropriate doses vary from a drop to more than 100u per shot - I've seen all of those here in Lantus/Lev Land. Sometimes vets haven't seen cats needing higher doses of insulin - many people euthanize cats upon a diabetes diagnosis so sometimes vets don't have a lot of experience with dosing a diabetic cat. Not saying that's your vet's situation, just mentioning it.
However, I understand wanting to take your vet's advice. I would watch carefully to see if you get lower blood sugar within 48 hours or so. Or ask the vet how long it should take for the antibiotic to take effect and the blood sugar to lower in response. The problem with waiting too long is that high blood sugar does do damage in the body, so you don't want to wait too long to see if one strategy is going to work before simply increasing the dose. How long is too long? I don't know - it probably varies depending upon the cat's body. These are things to be aware of.
Punkin developed C. Diff from getting clindamycin, so it's really good that you're going to give Rudy a probiotic! He got it for a dental infection after teeth were pulled. Clindamycin works on anaerobic bacteria, the kind that live in no-oxygen environments like gum pockets or intestines and is very effective. It can cause diarrhea if you haven't countered it with good bacteria, so be on watch for that. This is a really great link about giving probiotics to cats:
http://www.ibdkitties.net/probiotics/ I give them to 2 of my 3 every day. I've seen the suggestion to give the antibiotic, then 2-4 hours later give the probiotic. You don't want to give the probiotic first because then the antiobiotic will kill the probiotics.
Another thing to get on hand in case you need it - Sacromyces Boulardii. It's a beneficial yeast that will prevent diarrhea from the C. Diff and actually can overcome a C. Diff infection. I didn't know about it back when Punkin got sick, but one of my daughters has Lyme disease and has been taking constant multiple antibiotics at the same time for over 2 years now. She had one round of C. Diff more than a year ago and then we discovered S. Boulardii - which has prevented her from having that again. It's mentioned in the link above. You can buy it at a local natural food type store - it's common. You can also give it as a preventative instead or with the probiotics. There are directions in the link.