Hello BF,
I know that other Trek 620 owners have successfully installed 700c wheels on a Trek 620 that was originally spec'd with 27" wheels. As an experiment I mounted some 700c wheels that I have and took the photos below. The canti brakes are the original Dia Compes and they actually work well with the 27" wheels and were pretty easy to set-up.
In the photos the brakes remain in the position adjusted for the 27" wheels and I don't want to mess with them without some reassurance that it's worth the effort.
Do you think that adjusting them downward to the 700c rims will work?
Thanks.