The wheels that are called 27 inch and are tubulars are really 700C tubulars. The radius to the braking track on the side of the rim is the same as for a 700C clincher. It's a few millimeters less than a true 27 inch wheel. You should be able to just pop in your tubular wheels, check the brake shoe spacing, and go.

Just in case, are there any size-related markings on your rims? What kind of rims are they?

If you read off the serial number of your frame and find it on www.vintage-trek.com, you should be able to find the original catalog pages and read the parts spec for that year. Keep in mind Trek changed part and frame specs, often drastically, from year to year.