Great news! Things to consider on timing. First, you don't give R on the same cycle you do an L increase. Which would be Wednesday night if you didn't listen to the vet. Though you could delay the L increase a cycle. You also don't want to give it if he's breaking a bounce.
Could you try it tonight? I'd give 0.25 units R at the same time as the L, and test hourly for 4 hours after. You will also need to build a routine for making sure you keep the R and L separate. We have some people give the L dose of R.

I had Levemir in cartridges and R in a vial in a different part of the fridge, so it was easy to keep separate. Some people load the syringes and lay the L on a sticky note with L on it, the R syringe on a different colour with R on it. Just find some routine to keep them separate.
Things to consider with an IAA kitty - this will be a new insulin and may at first confuse the antibodies. You could get a strong initial reaction, part of the reason for a small starting dose. Second, some kitties, especially with IAA, have a stronger reaction the cycle after giving R.
The nice thing about R, is you don't have to give it if you can't monitor that cycle.