Originally Posted by Bklyn

• Before I get too far into this, I'm not imagining the superiority of side-pull brakes to center-pulls, am I?
As stated earlier center pulls are fine with new pads and alloy rims.
• The wheels are 27". Reach would be a problem only if I had switched to 700c wheels, right?
Correct. Assuming the new caliper you want to use is the same reach.
• Are there any issues I'm not even considering? Will the bolt on, say, a Shimano Ultegra side-pull be either too short or too fat to work with my fork?
Being an early frame I would assume the current center pull caliper does not have a recessed brake bolt and uses a nut on the outside rear of the fork. If the new caliper is for recessed your going to have a problem....You'll have to drill the fork or swap a different bolt into the new caliper.