This is very normal, and just to set expectations will likely happen for quite awhile (as in month(s)) - a stretch in good numbers, followed by a few cycles of bouncing, back to good numbers, rinse and repeat. Over time he should bounce less often, less harshly, and clear them more quickly. Not all cats do, but those cats tend to have underlying issues making regulation a little more complicated.
I know this is much easier said than done, but please do not stress too much about the BGs themselves. Ketones are more complicated than just the BG. You are doing everything you can, his body has to do the rest...I know it sucks to have things out of your control. Speaking of which, I would ask your vet about budesonide for that inflammation. I don't like that that wasn't addressed at all.
I have two babies/toddlers, expecting another here in a few months, a temporarily disabled husband, plus a complicated cat - I perhaps know better than anyone the cumulative consequences of all the broken sleep and stress. It is not good for anyone if one day you crash and burn!