Vintage Horticultural and Garden Machinery Club

Number of points; do not get yourself fixated on modifying the choke plate. If it was a generator or pump with a throttle and choke combined I would think about it, but as it is a Wheel horse with a manual choke do not bother. In all honesty quite a lot of them fire right up on tick over without any choke at all.
Remember the old ad-age; the majority of fuel problems are electrical. Make sure the points and condenser are ok and the ignition timing is correct. You have already received some good advice on the valves. Before you start taking the engine to bits too much, re-set the valve clearances. Too often valve clearances are ignored, the valves hammer in and have no clearance, make absolutely certain that the engine is on TDC when you set them (Top Dead Centre)
If you have access to a cylinder leakage tester this will allow you to hear if any air is passing the valve seats, a tiny bit is normal.
I am assuming this is a K or M series engine, that being the case it will have a Kohler or WALBRO carburettor fitted which are all copies if the original Carter carb. The WALBRO is different in many ways due to the emission controls incorporated into it, that being said the best way to describe these carbs is simple and crude. The main issue is that they do not have an accelerator pump which would shoot a small amount of fuel into the engine intake when you open the throttle stopping the hesitation which is caused by the sudden opening of the throttle making the mixture go lean. Anyone who has owned a Ford Cortina or Capri circa 1968 to 1975 will know all about this, in reality it over fuels the engine for second, creating emissions that are not wanted.
The last but important thing to remember is that K and M series do not like the mixture lean or having the ignition advanced. Depending on which cylinder head you have a nice hole about ¾ inch diameter will burn through the top of the piston.