$3,000 for a “newer” shifter to go racing with would be tough to find.
But for autocross, you can probably get away with an older kart… which “can” save you money and allow you to find what you’re looking for if you’re patient. I say “can” save you money because while some older karts have been well maintained (what you want), many haven’t, and by the time you get them prepped, you’re often better off with a newer kart from a cost perspective.
I don’t know much about autocrossing with karts, but several reasons why I would suggest an older kart are that I don’t think they require updated bodyworks and bumpers, and you might be able to get away with engines, and engine accessories (pipes, silencers, airboxes, carb, etc) that aren’t legal anymore in some of the karting orgs, etc.
As long as the brakes and the engine are solid and nothing on the kart is bent, you should be ok to autocross.