Quite often, an engine is selected upon availability- ie "I found this bike cheap so that's what I'm using". If you actually are in a position to shop around, that's great.
Unless your wealthy and dont care, you'll have to pay top-$$$ for most any specific motorcycle engine whether its new or used.
If I was building a kart like yours I'd just start watching my craiglist motorcycle ads and try to find a complete motorcycle that's either been wrecked or maybe the frame had cracked. You'll end up paying less for one of these than just an engine from most any source besides maybe from a motorcycle thief... This way you would hopefully be able to see/hear the engine running before buying it too.
You'll find there's lots of parts from the bike you could use for your kart like the complete brake system, air cleaner, pipe, throttle/clutch cables, kill switch, coil, radiator/hoses etcetera. You could even cut the bike down to just the portion of the frames motor mount cradle, and simply bolt that (in a sliding mount for chain-adjustment) to your kart instead of building the motor mounts from scratch.
With that said, I'd try to find a single cylinder 2 or 4 stroke street, enduro or mx bike between 250 and 500cc's so the engine would be narrower and lighter weight.
Does your reign of Kentucky require
all off-road vehicles to have an OHV type licence plate like
all of California and Arizona? (Az. OHV info here:-->
http://ohv.parks.ca.gov/?page_id=25733
If your states laws are like Arizona, the title you got with the complete motorcycle would make getting an OHV-type license plate much-much easier...