Melissa,
It's as if you are asking us for a second opinion on the diabetes diagnosis and everything else your vet did.
Vets want to check for infection with a diabetes diagnosis because infection/inflammation + not eating enough + not enough insulin is the classic setup for ketones to develop and that can lead to DKA (diabetic ketoacidosis). Very dangerous and life threatening. Your vet was trying to rule out that immediate possibility with more bloodwork. Not to say that DKA or other co-morbidities can't/won't develop later with a cat.
In my mind, I have absolutely zero doubt my foster cat had diabetes. And he had the diabetes for months and developed severe diabetic neuropathy and could hardly walk.
Blood glucose high enough to dump excess glucose into the urine is one sign of diabetes, but the vet was also testing your cat Freckles urine for specific gravity, for color and clarity, for all sorts of other "clues" that could help in the complete treatment of your cat and all her conditions. "Treat the whole cat."
The change to a low carb food could have made all the difference with the diabetes. Yes, we have seen the BG numbers improve that quickly with a change to low carb food. Open my cat's SS in my signature. You'll have to go over to the right and click on the 2012-2013 tab. Look down after 1/15/13 and start looking a the BG readings and the notes. He was a dry food addict at that point. Then keep looking down the SS as I was transitioning him to low carb wet food and you'll see how rapidly he dropped into 'normal' BG ranges.
Not the best example of a SS to look at, because I was fighting, literally fighting, against the shelter and their vets to 1. test more and 2. get him off the high carb Hill's W/d dry food they had prescribed. 3. lower the dose more rapidly than the shelter wanted me too. Good thing I did, or he would have died.
Remember, we are not vets, only laypeople that have had cats that were diabetic.
I think the best thing you can do now is keep your kitty on the low carb food, try to keep testing and ask your vets any questions you may have via a phone call or at your next appointment.