Been looking for a rebuild kit for your bike, harder to find than I'd thought, but found one here,
https://www.denniskirk.com/parts-unl...prd/174981.sku. According to them this kit fits all GZ250s from 1999 - 2010. I can't vouch for that, as I said I haven't rebuilt, or even had a need to clean mine so haven't ordered any carb parts. But you should be able to look at the pics on the page and compare to what you have seen on your bike to give you a good idea if it's the right kit. No floats in this kit though. Floats are not normally provided in rebuild kits since seldom needed. If your's r truly bad you may have to order them separately.
Have to ask you one more time about the petcock. When engine is not running and valve is set to On or Reserve no fuel flows, correct?
BTW, before spending $200 on parts to rebuild your carb, I'd look into just buying a new carb.