Choking it (either via choke or changing carb inlet) will make a minor difference for just a couple seconds but it'll hunt and stall either way. It's hunting so much that it's hard to tell if it's making it better or worse for the short duration.sounds like a fuel starvation issue. Try pulling the air filter and cupping your hands closer and closer to the carb inlet as it starts to surge. See if that affects the behavior. If the engine smooths out as you move your cupped hands closer than it is running lean. If it gets worse then it is rich. I had something similar on a pressure washer and a new genuine carb solved the issue. Actually it took two because lots of old stock stuff has been used before. Someone told me that I should also look for cracks in the inlet manifold if it was plastic. Mine was aluminum but a small crack would be easy to over look. Also if one has a loose head it can cause similar behavior. The compression on the pressure washer went from about 30 psi to about 100 psi when I replaced the head gasket and adjusted the valves. Remember that valves grow as the heat up so if they are tight that can be an issue too.
When I had the intake manifold off (mine is plastic) I did check it over carefully for cracks. Didn't see anything, but I didn't have a good way of pressure checking it or anything either.
Haven't checked the head or compression on the valves. If the alternative gas source doesn't fix it, suppose I can check that. The mower only has about 30 hrs on it and it ran fine for probably the first 20 (mower is a few yrs old, so despite lower hrs the warranty is up). When I had the intake manifold there were no signs of a burnt valve or excessive buildup that would change the valve seating. I've never had to adjust valves on one of these B&S VTwin's before - including the 15 yr old John Deere I've got. It looks like a pain from the service manual - remove exhaust, governor, remove and mark push rods just to get to one of the cylinder heads. Gaskets need replaced so rebuild kit. Also appears as if the threads are all using Loctite 242 and torqued 100 ft-lb, so they shouldn't have been creeping to start out with. Is it common in the VTwin's to have some kind of misadjusted valve or head gasket leaks?