Sorry, I was answering someone else. It can take a few minutes for me to get back to you.
If you hold the governor rod so that the throttle is at normal operating speed and the engine dies or surges, then it sounds as though the carburetor could stand a good cleaning. I'm assuming it does this with the air filter off? It only takes a speck of dirt in the wrong place to cause a carburetor to malfunction. What you can try is to spray a little carb cleaner in the carburetor with the engine running and see if that helps smooth it out. If it seems to help, then a product like SeaFoam used per the label might be of help. This may save you from having to completely rebuild the carb.
If holding the governor stops surging, it could still be the carburetor, but also could be an internal problem with the governor. Since the carburetor is cheap and easy to work on,. I'd eliminate that as a source before I moved to the governor.
I'd try that. I forgot to ask, which engine is this? If the SeaFoam doesn't help, then I'd pull the carburetor and check the float level. While I were at it, I'd go ahead and give the carb a good soak in a tub of cleaner and put a new kit in it. As there was some sediment in the bowl, it's a safe bet that there's more. All it takes is for an air circuit to be partially clogged and you'll have your problem. Also a leaky intake gasket can cause this sort of trouble.
After being completely satisfied the carburetor is okay, then your two options are to check the head, valves and head gasket and the governor. It's fairly uncommon to have a governor malfunction, but it does happen. Let me know what you get with the carb and we'll go from there. Thanks, PK.
I just saw your edit. Yes the intake gasket can cause this. If the carb was off and a new gasket wasn't used this will cause a surge.
You can check it by spraying some carb cleaner at the mating surfaces with the engine running. The engine will speed up or die or smooth out when you do this if there's a leak.