So... the Trek 720. An 83 would be first year with cantilever brakes and last year with the old school Trek styling.
The Sugino AT is one of the best, and best looking triple cranksets ever made. Check out Sheldon's database-
https://www.sheldonbrown.com/bbsize.html.
I seem to remember it being 127- but there's other values in there. I've had several half step/granny crank sets but don't use them exactly in that context- but I will use the half step to find a more comfortable cruising gear- and only with 5 or 6 speed. I'm running 10 speed so my crank rings are 28-38-50. But I probably should be running a 48.
As mentioned- a 1983 Trek will not be spaced at 120- most likely 128 and you can use 126 and 130 with none of that "cold setting" nonsense- on top of it only being 2mm- it's 2mm with 47cm chainstays.
Yes you should be able to use a Cyclone GT (either first gen or MII) with 7 speed. The suntour barcons will work with that. I'd suggest getting real shift housing rather than the metal springy stuff it came with. I haven't used the old barcons with anything over 7 speed- you might have a bit of an accuracy problem at 9 and over. Again, half-step with 7 speed is dicey- someone can figure that out with a gear calculator.
Me, personally- if you're running the original DC960 brakes, I'd replace those with something cooler- XT M732, Deore MT62 or MT60 or XT MC-70- in that order.
I have a 1985 Trek 720- I've replaced most everything on it- but it's running a 10 speed triple. It's really a great great bike.
1985 Trek 720 by
Dave The Golden Boy, on Flickr
85720Yard by
Dave The Golden Boy, on Flickr
IMG_0616 by
Dave The Golden Boy, on Flickr
IMG_2402 by
Dave The Golden Boy, on Flickr
IMG_1728 by
Dave The Golden Boy, on Flickr
IMG_1715 by
Dave The Golden Boy, on Flickr