I went down the used sidecar road a few years back. For about a year I could not find one on CL or Fleabay. Gave up my search for used and then I found an Cozy importer in Texas that could save me about $900 on a new car from the sponsers of this site. Gave the guy a deposit and 8 months later no car and no word, called and was told they were on the way from India. 2 months later called and got a different guy and talked to him, they had yet to order the shipment because they were waiting for 2 more deposits (and buyers).
Got my deposit back, called CMW and they had a sidecar delivered to my driveway a week later. Bolted it to my RE and all is good.
I also experimented with a CJ sidecar (same as ural but with leaf spring instead of shock). At the time I was tight on money so I hooked it to a Kawasaki I bought cheap. Worked but the bike was rev happy (KZ650) and I just did not like the setup. Sold the car and bike seperately for a profit.
If I had that tub still I would hook it to a Sportster 883 and then upgrade the jugs to 1250 for a few $100. The sporty would be reliably, geared right (883s are geared lower that 1200s), parts are everyplace and it would haul ass. Around here you can pick up a used 883 for about the price of a new Cozy if you look hard enough.