Most of the time, based on what I have seen on others and on ours when we still had it, the surging is caused by a mostly plugged up carburetor in the very small gas internal passages. It happens worse and much faster if you have to use gas with ethanol added like we do in Minnesota.
As long as the engine will still run, albeit poorly, you do stand a pretty good chance of fixing it without removing, or even looking at, the generator itself.
Running the engine on new gas with a cleanout dose of Seafoam additive has fixed many Onans over the years, including ours.
1. I think the best way to do it is to use up as much of the existing gas in the van that you dare do if it is more than a couple weeks old.
2. Fill the near empty gas to about 1/2 full so you have enough to let the generator run.
3. Add enough Seafoam to the gas tank at the cleanout rate which is about double the storage rate. It will take quite a bit.
4. If the engine is prone to killing when a load is on it, don't do that for a while.
5. Start the Onan with no load and let it run 20 minutes with the gas and Seafoam going through it. There is no need to go longer than that.
6. Let the van and Onan sit 24 hours and repeat the 20 minute run. If it has smoothed out some, try putting a fairly small load on it and see how it does. If it carries the load and doesn't kill you know it is helping.
7. Let it sit 24 hours and repeat the above but after 5 minutes put on the small load and if it continues running add more and more load until it either starts surging horribly or dies. If it does run poorly at higher load, back off the load and let it run the rest of the twenty minutes at the reduced load.
8. Repeat number 7 as many time as it takes to get smooth running under load.
9. If it gets smooth at all but full load or sags in rpm when you put on the full load, you might be able to take care of that by removing the cover of Onan and setting the elevation knob on the carb to a lower elevation. This will richen the mixture and might be enough to take care of full load issues or a big sag in speed when the full load is added. Ours needed that change.
10. If the Seafoam fixes it, to prevent it from happening again you will need to add Seafoam to the tank any time it is going to sit anything more than about 3 weeks if you have ethanol fuel in the tank and Onan, but you can use the storage amount for that. When it is going to sit, add the Seafoam and then run Onan until at least completely warm. The generator should be run for at least 20 minutes once a month per Onan, and I think that is important if it sits outside where it might get moisture and condensation on the slip rings section of the generator which will corrode them. Our van sits inside in a heated shop when not in use so doesn't see the radical temp swings that it would outside in Minnesota, so we were able to run the Onan much less often. Whenever you run it after storing a while it is good to have Seafoam in the gas, but it can get expensive to do. Buying a gallon at a time can help on the cost many times.
Let us know if you try this and how well it worked, or not, for you as that is always interesting to know.