Wondering what stoke components are.

630x32 and 27x1 1/4 are two ways of specifying the same size. 27" wheels were the norm in the 80's. Most/many tubes for 700c tires will work with 27" tires. They will be labeled for both, most likely. They might say 630, also.

Taking off the tire and tube after the first puncture and looking for the problem would have been a lot less messy than fooling around with green slime.

Tread doesn't prevent punctures. 'Slick' tires are fine for paved roads and many other surfaces. A lighter flimsier tire, however, will be less durable than a beefier, heavier tire. A compromise is a light tire with a kevlar belt under the tread.