I have gum-wall 27x1-1/4 tires by CST that look very close to the original Schwinn tires, I use them on Varsity, Continental, and Colegate, ride well and look right. $48 / pair delivered in USA
PM me if I can help.
I would vote for the CST. While I love Paselas, a skinwall tire is just wrong for a Varsity. My first 10-speed was a '69 Varsity and I think it came with blackwalls, which would have been the Breeze. I wrenched for a Schwinn dealer through most of the '70s and, as I recall, Varsities came with gumwall Puffs for most of that time. I disliked the Puff at the time, as it was hard to seat properly, but Schwinn did a good job of matching it to the bike. The Suburban, Varsity and Continental were designed to be rugged, long-lasting, yet affordable bikes. There was nothing about them that I could see that was intended to make them exciting to ride. The CST is a well-made, affordable tire, and I've had some that had a layer of rubber over the sidewall, similar to the original Schwinn tires. The CSTs are definitely a cut above the Puff in performance. Unlike the Paselas, they won't cost more than the bike is worth.
Shops stock what sells and if there is little demand for a size or product, it's likely a poor investment for the shop to keep it on the shelf. I know of no advantage that the 27" has over the 700C. The difference in radius is only around 3/8". On the other hand, with so few people still riding sewups (myself excluded), the previous advantage the 700C had in being the same diameter as a tubular rim is no longer applicable. Still, the 27" was always a relic of a bygone era, after the world more or less standardized on the French A, B, & C sizes.
In 1977, I ordered a Paramount touring model, as I was planning on a cross-country ride that winter. I gave it a lot of thought, and finally decided to order it with 27" wheels instead of going with the "new" 700C size, thinking it might be difficult to find 700C replacements in some parts of the country. I have always regretted that decision, especially since I never needed to buy a replacement tire on the road. I don't ride that bike much these days, as it has other, more egregious flaws, but I have always wished I could go back in time and correct some of the mistakes I made in that Paramount order.