replacement engine

It doesn't sound like a terribly good price to me, but I suppose it depends on whether you can install it yourself or not. No idea what shops charge for the labor aspect.

I bought a used HMSK80 for $150, and it came with a free Ariens ST824 snowblower attached Paying over 3x that for just an engine doesn't sound very good to me. You can buy a whole different used Ariens snowblower around here for less than $525. Then you'd have an engine as well as a second machine.

There seem to be a lot of machines that use those engines. Be aware that some HMSK80's have a second output shaft, to run another belt. So you'd want to be sure of which version you need (just a crankshaft output, or crankshaft and this second shaft).

If you were interested in using a different, new, engine, there are a lot of Chinese clones which could be options. But that will be more of an undertaking, quite a bit more involved than simply swapping for an identical engine (making sure the engines interface the same way, maybe rerouting controls, etc).

What's wrong with your engine?

If it won't slow down much, can you tell if it's running at the proper speed, when the throttle is up? In other words, is the problem that it won't speed up, or it won't slow down? You might be able to find a YouTube video of someone blowing with an older Ariens, to get a feel for what it should sound like, worst case. Presumably, like you said, it runs properly at full throttle, and just won't slow down. Hopefully the shop would have mentioned something if it would not speed up beyond idle or something.

I have a Tecumseh that's a few years older than yours. I did actually check the valves a few years ago, and found that one valve had less clearance than it was supposed to. I took it out, and we machined a few thousandths of an inch of its length. Reassembled and it had better clearance, and more compression while pull-starting (the valve wasn't being held open as far by the compression release). I want to say it had a bit more power afterwards, but that could have been my imagination.

Checking the valves was not hard. There's a cover on the side of the engine which exposes the valves. You just need a set of feeler gauges (inexpensive at an auto parts store, etc). To adjust them, on the other hand, is a fair bit more work. But checking them might show them to be fine.

I would consider that you might have a carburetor/throttle issue. There's a big cover on the left-hand side of the engine that covers the carburetor and throttle linkage. You could pull that off and see if the throttle and governor are moving smoothly, to make sure nothing is binding up.

If it's not revving up to the proper speed, and it's just an adjustment problem, there's a little screw that's visible if you raise the throttle lever. You can use that to adjust the full-throttle speed. There is also a screw under the cover to adjust the idle speed. But I wouldn't start messing with those just yet, if it were me.

There are a lot of knowledgeable and helpful people on here that can help you out.