Updating a classic Schwinn Voyageur SP

I've got a classic, circa 1982 Schwinn Voyageur SP touring bike
with about 70K miles on it. It has been my trusty daily commuter, and
touring bike since I bought it new way back when. It has 120mm rear
drop-out spacing and 27" wheels. I'd like to bring it up to date so
that I can shop for parts in more bike shops than just Recycle Cycles
(nothing against Recycle Cycles).

I know I can cold-set and realign the rear dropouts but I was
wondering about whether I can replace my 27" wheels with 700C wheels
and have the brakes still align with the rim. I want to move up to
linear pull brakes instead of the calipers I have now. I tried a 700C
wheel on the bike and it looks like the rim is about 1/4" shorter on
the radius, so my brake pads overlap the edge of the rim by that
amount. Any suggestions?