Haha welcome to the teacher club! Former teacher here.
Not sure why the vet would say it takes that long for a dose to be effective. It's not true. I don't think any insulin takes that long to take effect..we see cats who needs a few cycles to settle in to a dose, but never that long. Actually, what can happen is that he sits in these higher numbers for awhile and then develops a bit of insulin resistance...where he just has these high cycles. My guess is you may be seeing that here.
I'm with everyone else. I'd up his dose when you can monitor (maybe tonight?) and then go up every 3ish cycles (just making sure you can monitor when you go up). Once school lets out it might be easier for you since you can monitor more during the day then if you increase in the AM. We usually suggest holding for 6 cycles, but with your higher numbers, I'd say 3. I know it seems like a lot, but usually with insulin resistance, we see these higher numbers, and then one day, they just hit the right dose and start sliding back down the scale! Let's hope that happens here too!
One other thing, are you testing for ketones?