You can build up the Campy hubs to any rims you want (with the correct number of spokes of course.) If you go this route, I'd suggest the 700c size since you'll have a much larger choice for tires. 700c rims and 27" rims are virtually the same size so your brakes should reach unless the pads are already at the bottom of the calipers.
It's unfortunate your rims are straight side, because it would be much easier and cheaper to just search for some nice 27" tires. I have never used straight sided rims so I can't help you there, but if you're willing to run 70-75 psi I'd say give it a shot. IMO that's plenty of pressure for a 27 x 1 1/4 tire, but I am also a lightweight.