I am having issues with my 1050 surging under load. I find only a parts manual, I thought we had a service manual in the past.
Are new Zenith carburetors even available anymore?"Surging" under load is I have found typically a carburation issue. I have dealt with this on my 900 with S8D and a couple of others. I bought a "carb kit" for all that was worth and put it in the 900 carb and it was ZERO help. Carb kits are usually only good for gaskets IMHO. On three surging engines (all Wisconsin, one an AHH), the surge was caused by wear of the throttle body shaft holes causing a mixture change that would make the governor surge back and forth. The wear is something that just happens with use and vibration over time. The shafts are mild steel and the carb is pot aluminum. Lets face, the designers really didn't think these things would still be running a half century later.
Excessive lean mixture causes hotter combustion therefor increasing power. With the surge in power the governor reacts and cuts the throttle back. When the power falls to low the vicious cycle starts again.
There is a detrimental side effect to excessive lean, which of course is hotter than design combustion gasses which in turn cause burned valves, valve seat damage and premature cylinder wear.
My final remedy, that worked, was to purchase a new carb for one of them, another I bought a parts carb and used the upper half with good tight throttle plate shaft and the other was bushed on the throttle plate shaft. Bushing can be done to restore dimensions but it is tricky with the smaller carbs as not much material is there to work with.