Looking at the photos of the bike, I have to say, yep, that bike was made for 700c wheels. But if you can get tires that fit and the brake pads properly hit the rim sidewalls, then by all means continue to use your 27" wheels.

The skinniest 27" tire I'm aware of is the Continental Ultra Sport in 27x1-1/8. If a local shop stocks Continental but doesn't have this size (27" is considered obsolete), they should be able to order them for you.

By the way, that's really sweet ride. You know how to pick 'em.