Well the select drive of the HRR and the HRX217VKA are both belt drives for the self propel system. The HRX217HYA is a shaft drive system. The shaft drive basically doesn't have a belt to wear out, so it will last longer and hold up better over constant use. That's why it's in the commercial series. The Honda belt drives though are really good. I had an HRR216SDA that the belt lasted 15 years and then I replaced it myself for a cost of $12.
As for your HRR it's probably either the belt is bad or came off the track, the cable could be loose or broken as well. As for the running problems you can do the normal carb cleaning and double check you don't have any debris in the gas lines and tank. That sounds fuel related assuming your choke is operating normally. There's plenty of youtube vids showing how to do these things so I would give the DIY a go before dropping a lot of money.
There are three different versions of the Honda drive system.
I currently own the HRRVYA which has the smart drive and roto-stop blade brake system. I didn't particularly like the paddle style of engagement, but it worked. I'm trying to understand how the smart drive, the select drive, and the hydrostatic are different.
I thought all three of the transmissions were belt driven, and that the only shaft driven version was on the HRC - the commercial model which starts at about $1100.
Regarding the HRR, I'm generally pretty repair savy. I feel comfortable doing timing belt and head gasket repairs on an automobile.
I had an issue before where the HRR was running rich and would carbon foul the spark plug. I replaced the spark plug, the air filter, the carb, the choke, the thermowax piece, and all the applicable paper gaskets. It worked okay afterwards but still wasn't quite right. I've been running 89 octane non-ethanol fuel (I use 89 for my stihl stuff so I just get all the same octane) with stabil included. I've taken off the carb, sprayed with carb cleaner, and sprayed out with air. Best case, I've got some dirt stuck in the carb that I manage to get out, and then adjust the belt to get the transmission working again.
If the engine was running well, I'd be happy to go about resolving the drive train issue. However, at this point, it doesn't start, the wheels are worn smooth, and the self propel doesn't work - Is there a point where you just decide F it and move on?