Update:
The primary nut, counterweight nut, and clutch nut torque specs were all fine. Sharah retorqued them anyways but it was unnecessary.
We did discover however that the kickstart mechanism was a bit funky. When fully reassembled the kick lever mechanism would only engage very close to the bottom of the down kick. Only about 1 out of 6 times would it catch at the top and allow for a full kick.
Digging back into the case we realized that the spring and helical splines of the shaft and gear did not engage with every turn of the shaft. It was also noticeable that the kick starter gears and the starter idler gear were not meshing correctly and that they each had damage to their teeth.
The aluminum shavings we found were quite possibly from the kickstarter grinding inside its seat and from the spring grinding against the case interior on each kick rotation.
I'm still unsure if this will resolve the other rotational whining noise while the engine is running, but it's a start.
So, it was off the ebay races. However Ebay sellers wanted an outrageous $350.00 USD for just the kick start mechanism and lever! When asked about their high prices the seller claimed that new TW200 bikes don't come with kick starters installed and the owners are willing to spend the money to retrofit their bikes with these old kickers.
And that's how we ended up at a junkyard.
There's a somewhat well know known motorcycle boneyard here in Salt Lake City called Bill's Boneyard that is the most massive, sprawling collection of Japanese motorcycle parts I've ever seen in my life.
Bill showed us around his property and pointed out the likely places where we could find an XT200 motor. Outside are three or four piles of motors like this
Inside the deep, dark shop are shelves lined wall to wall, floor to ceiling with motors, tanks, plastics, fairings, and everything else motorcycle related.
During our second pass through the shop we finally found what we were looking for - a mostly complete, non-seized early 80's XT200 engine, with intact kickstart mechanism. Bill looked it over, spun the crank by hand, and suggested a retail price of $80 for the lump.
Sold.