I bought mine new in 1985 a TREK 720
It will run Michelin 35-630 tires (27x 1 3/8) as shown on GMS's 720
except I can no longer find any Michelins in that size
or any road tires in that size.

Currently running Michelins 32-630 which measure 33mm wide.

I slapped a 700c front wheel from my wife's bike
with a 22mm wide rim (700x38C tires {which measure 35mm wide}) and the brakes needed very little adjustment.

I am thinking of having the rear coldset to 135mm and going the 9 speed cassette route with 700C wheels. The original Helicomatic is still running fine.

Alternate plan keep the 720 as is and buy a Surley Long Haul Trucker.
My TREK fits me with a 1mm standover height that may lead me to a more appropriately sized Surly.