This must be the old 3 speed forward 2 reverse - like a 38040? The problem is, that I've forgotten more than I seem to remember being out of the snow belt for a while. I can offer a few tips though. before you do the adjustment in question, the handles must be secure and square at thechassis. In addition to the link, I believe there is a knuckle under the panel where the shift gate is that can be adjusted also. On the underside, bushings need to be tight and the drive plate must be true. I suppose that the spring on the carrier could be weak. Hope some of this helped.

You may have long ago fixed this, but I had the same problem with my Toro 824. I kept what I did in my diary, as follows:
After all the usual adjustments and suspecting the friction disk, eventually I decided that the drive pulley was riding way too close to the auger pulley, and found that there was too much slop or "play" in the main drive shaft, on which all the pulleys and drive contact points are mounted. I came to the conclusion that the far rear end of the drive shaft was riding too far down toward the front of the machine. This moved the forward drive pulley too far forward as well, away from the friction disk. On disassembly I discovered that on the main shaft there was a roll pin that had sheared off, allowing the washers to ride over it and make all the mechanism sloppy enough to keep the friction disk from making proper contact. I bought a new roll pin from Toro for $3, and it made the drive mechanism run like new.
I hope this helps.