Also check the wheel ratchets. From what I remember the SXA was a 2 speed trans and they did develop intermittent slipping problems. One of Honda's untold mistakes. They would work fine and then would slip. Start working for weeks and start again etc.

You probably have nothing to lose if you clean it up and open to have a look. Normally Honda doesn't service internal trans parts, but maybe you will luck out.

I tried shifting the lever around between 2-3 and 1-2 but the only place it pulls real hard is in 1. What's in the trans. How can it work in 1 and not the other gears? Are there really steel gears in the trans, or does it work on some kind of fiber clutch system that may have worn out on only 2 and 3? I Don't hear any abnormal noises coming from the mower as if a gear tooth were broken.

Don't apologize for your post -- it's helpful IMO to have various Honda snowblower problems collected on one thread. Your problem falls outside my experience, but I can tell you how I'd start, at least. First, make sure your hydrostatic transmission fluid level is correct. I don't check mine as often as I should, and if it slowly dropped (or quickly due to a seal giving way or something) I might not notice right away. I have no idea whether low fluid could cause this condition, but checking it is a good idea regardless. Second, if you don't already have one, consider buying a service manual. You may be able to find one at a dealer but if not they can definitely order it or you can get it online. It may or may not help you diagnose this problem, but it allows you to approach any repair with greater confidence -- or figure out in advance that you're in over your head. Next, make sure you've got access to exploded views of the whole machine. You can find them using the link below. After that, flip the little transmission engage/disengage lever that you use to allow the machine to be pushed. If the problem persists with the transmission disengaged, it's almost certain that you have a problem internal to the transmission. Next, assess the overall feel and action of the controls. Does the drive clutch lever feel normal? Does it have that slight "over center" feel (i.e., a relaxation of the spring pressure) as you get it close to the handlebar? Does the normal interlock action between the drive clutch and the auger clutch work normally (i.e., if you hold the drive clutch and then engage the auger, can you release the auger lever without it disengaging until you release the drive clutch)? Does the hydrostatic transmission control lever feel normal and have its normal range of travel? If any of this is wrong, I'd start looking at the engagement levers and the adjustment of the cables. Beyond that, if it were me, I'd probably be looking for a pro. Good luck! Here is a link that might be useful: Honda snowblower exploded parts views