A lot of the John Deere equipment used the same engine. 345 garden tractor comes to mind as does the 285 garden tractor, among others. So there's a good possibility that a carburetor for a 345 will interchange. Try Deere part number AM122617. That is a number that came to mind, OTOH, and going off of my aging memory.
Kubota no longer supports Kawasaki engines; any Kawasaki engine parts that were once available through the Kubota dealer network are listed as "no longer available" through Kubota, so you have to get them from a Kawasaki engine dealer. When sourcing any Kawasaki parts from a dealer, you want ALL of the numbers off of the engine. FULL (not partial) model and serial numbers specifically.
Example: Model FC501V-BS00 and serial FC501VB23498 (etc).
When the Z122RKW-42 came out a few years ago, I was looking up an air filter for it and was quite surprised to find that it showed to be "no longer available"--as listed by Kubota's dealer system. A 1 week old mower and NLA. Since then, Kubota's updated their listing (at least through the dealer system) to where you point/click an engine part and it takes you directly to the Kawasaki system to look up the part. However, some of the older equipment, that's not the case, and a lot of times the dealer will just say "tough luck", perhaps because they're either too lazy to do the leg work, or they simply don't know....OR they're not a kawasaski engine dealer. All 3 are too common, in my opinion, particularly the first two.