I'm so sorry that Jake is having such a hard time right now. It sounds like you are doing so much to help him to feel better, and that is amazing!
My Figaro was diagnosed a month ago with diabetes and it has been a challenge, I completely understand not wanting to poke your precious kitty. Truly it does get easier. I couldn't even test at all, just a few weeks ago, and now I can multiple times a day, and Figaro will be better for it.
One thing I have read is that cats don't actually have lots of nerves on the edges of the ear, where we poke, but many are of course irritated by being touched on their ears. So when I started out testing Fig, I would rub his ears as part of his petting sessions (outside of test time) to get him more used to it. Treat after has been important for Figaro, if Jake doesn't have an appetite for food treats, is there some other reward like pets or praise?
Another thing, some people sing to their cats at test time to loosen their own nerves and calm the kitty as well. They can sense when we are nervous, so remember to take a deep breath and remind yourself that you are doing this for him, and go in confident (fake it til you make it!!).
Just generally, maybe you could prescribe yourself a set amount of uninterrupted quality time with Jake as part of his treatment... whatever he likes best, whether pets, or watching the birds, or you singing to him... just non-medical time, no reading articles about cat health or texting. Could just be 10 or 15 min. It's been important for me and Figaro.