Low profile tire suggestion for 27 x 1 1/8 wheels
There’s really no such thing as a low-profile bike tire, AFAIK. All bike tires take on a circular cross-section when inflated. You’ll need to use a narrower tire. Another more expensive option would be to switch to 700C wheels, which would give you another 4 mm of clearance (and a better tire selection). 

Cool bike, btw.