Did it have a Viton tipped needle, like a rubber tip, or was it solid metal? And what material is the seat?
The float must sit level with the base of the carburetor when you turn the assemble upside down. Did you check for this?
Surging can have several causes, poor intake seals, loose head bolts, leaking head, malfunctioning governor, poor governor spring tension, poor carburetor air flow, and others.
The thing to do is start with the cheapest, simplest and most obvious. That would be the float level if you couldn't adjust the mixture screws and eliminate the surging.
If it has an all metal needle then it should have a neoprene seat which has to be changed. I use an awl which I put a slight hook into the tip of for pulling the seats but any slender stiff wire will work. You pretty much have to replace the seat when replacing the needle if it does have the neoprene seat.
For checking the float, all you have to do is turn the carburetor upside down and see that the float is parallel to the base of the carburetor. There should be an even gap all the way around it. If you have a metal float, you can bend the little tab where it contacts the needle to adjust it. If you have a plastic float and it's off kilter even after replacing the seat let me know and we'll go from there.
One other thing I would ask is when you rebuilt the carb, how did you clean it?
Mineral spirits work well for cleaning carburetors. Especially if you soak it for an hour or so. Then rinse with water and blow out with air.
The engine will have a model number, like HSK40 or something similar and a number after that. Can you give me those numbers?
I'm in Tennessee, but everybody assumes Colorado.
To adjust the carb so it runs smoothly, turn the main mixture screw out 1 and 1/2 turns, crank the engine, set the throttle to your normal run speed and then slowly turn it in until the engine starts to run rough. Then back it out until it runs smoothly and then rough again. Then set it at the halfway mark of where it ran began to run rough. The trick is to turn the screw extremely slowly. It should take a couple of minutes to go from rough to rough.
Then set the throttle to allow the engine to slow idle and do the same thing with the idle jet, the one on the side.
If it's backfiring through the carb then it's running a little lean and that needs to be corrected as you can damage the engine from overheating.
I suspect winter is pretty close to Cleveland about now. Thanks and let me know if you need anything else, PK.