For track or wheeled: You probably know most of this but running through....
The belt goes under a 3-4 inch belt guard. I'm sure you know that as you can't get the belt off without loosening the holder bracket.
The drive clutch arm can be adjusted. The arm holding on the tensioner has a slot for the tensioner pulley which allows the tensioner pulley to be moves about an inch. With a new belt the clutch cable tension and the tensioner pulley should be able to be back off quite a bit and the belt properly tensioned with the clutch only.
Have you looked in there with a flashlight to insure everything is aligned anything bent? Tape the drive clutch down and look in there. With then new belt you should be able to tighten it and have things inline. I can't remember the detail on changing one like yours (HS70) but I think the front auger pulley was in two sections and the back one. Possibly that has slipped on the crank.
http://www.boats.net/parts/search/Honda/Snow%20Blower/0/HS80K1%20WA%20SNOW%20BLOWER%2C%20JPN%2C%20VIN%23%20SA1-1100001/DRIVE%20PULLEY/parts.html
Check drawing numbers 10, 11 and 12. They list 10 and 11 as belt stoppers but those may be guides, 13 is about the same. Check to see if they are in place on your machine.