Yep, tires. I couldn't believe the difference when I swapped tires on my Miyata 710. Yeah, they're 700c, but the point is still valid. When I changed from thick, heavy Vittoria Randonneur to Vittoria Rubino Pro Tech III, it dropped almost TWO POUNDS of rotating weight! The Rubino Pros also rode much nicer!
That said, I also have a '84 Univega Gran Tourismo - it now wears Paselas PT in 27x1-1/4. Nice ride for a 'flat-resistant' 27" tire.
FWIW, the Gran Tourismo rides pretty much like my beloved old '75 Fuji S-10S. Both have a long wheelbase, low trail, and a stable ride. Both are 29-30 pounds with rear rack, bottle cages, full-size frame pump and fenders - the latter a 'must' for touring!. Both are equipped (Fuji was 'upgraded') with triple cranks and 6-speed SunTour Winner Ultra-spaced freewheels. Both have friction-shifting SunTour barcons. I've always been a friction-shifting guy! The right chain can make a big difference. I < think > I'm using KMC X8 chains these days on both...
BUT, your '88 Miyata 615 is a refinement of the older Gran Tourismo. I had picked up one of those for my niece, and it rode quite nicely with it's indexed Shimano light action shifting. I'm normally not a fan of indexed shifting for various reasons, but when they're set up right they are nice.
Bottom line - try tires and a newer technology chain. Oh, and newer Teflon-lined shifter cables with slick stainless inner wire - you'll thank me later!