I've run 700c x 37 CONTIs in a 56cm TREK 420. The tight point is the chainstays.
I've also run a 700Cx38 in an old NISHIKI. The limit there was the brake bridge.
A great deal of the fit depends on the rim width. A wider rim is going to make the tire "taller", as in closer to the brake bridge.
If you are looking for a bike to run your tires on, the TREK 420 will soon be posted FOR SALE in the C&V pages. (on eBay i see them selling for thousands and thousands of dollars!! .... no, not really....)
Here's some pics. The one with the 'DETROIT BIKES' headbadge is the NISHIKI. It could be for sale, but it's in another city waiting for me to visit the in-laws, so more complicated....
trek
trek
trek
nishiki
nishiki
Nice pics. Yeah I am thinking that an older Japanese bike originally built around 27 inch wheels might be the way to go. I like vintage Fujis.