Given the era of the Crit bike, I would hazard a guess that 28mm would be the max you could put in, maybe only 25mm?
It will be interesting for you to try modern bikes with faster tires that roll really well, and compare directly with the old bike. Nostalgia may take a back seat when you directly ride one after another.
I know it's small details, but when I put 32 supremes on my cross bike that what's had 28 gatorskins, the ride quality difference was noticeable-- and there are all kinds of great tubeless tires out there that I'm sure you would find amazing to ride.
Just don't forget, initial impressions may feel slower due to not having the "fast buzz" but real speed numbers in the real life real person (ie not pros) range will be pretty much the same with a fair comfort increase, which means more endurance because less physically tired and best up.
And as you say, add in the additional dog years!