Is your vet's hospital a 24/7 one? I would not want to leave a cat getting insulin where there is no one checking on them overnight.
The usual starting dose is 1u. It is not possible, in a few days, to reach the optimal dose. So, this vet boarding/observation thing is a waste of time and money and stresses the cat. It takes time to reach the best dose as insulin is introduced and given a few days to start working - then the blood sugar is tested and a dose change figured out. Yes, most cats need a dose increase every week or so for a while, but they should be small increase (.5u or less) in most cases. You can learn to test his blood sugar at home using any human blood glucose meter. Walmart and Target both make one where the test strips are cheaper.
What are you feeding him? Dry food would be my guess with numbers that high. Dry food is loaded with carbs, especially the cheap stuff, but ALL dry food is too high in carbs. The Fancy Feast Classic flavors are a good food as they are low carb and wet, which much more closely matches natural prey (mice, birds, etc.), but you don't want to change his food after he starts insulin unless you are testing his blood sugar because insulin needs can dramatically drop. Sometimes just a diet change and a few weeks on insulin can put the diabetes into remission.
You probably want to find the FAQs and read up on feline diabetes. There is an FAQ button on the top, right side.
I really encourage you to take charge, learn to home test (we can coach you through that), and change his diet to low carb wet food.