Hi Jim, Do you think the fan from the 14.5hp engine will fit to replace your broken one? I would not try the flywheel from the 14.5hp engine though, just the fan....
Regarding the head from the 14.5hp engine, I understand you to say that the cylinder diameter is smaller, so the corresponding recess in the head is smaller? If this is the case, as long as you can get a good seal with a gasket to the block, I would give it a try for sure.
On the surging issue, we have ruled out an intermittent kill switch with the test you ran earlier.
Have you looked into the carburetor? I thought I saw that you swapped it out earlier... but I am not sure.
I had an Onan on a JD 318, where the intake manifold was pressed together and glued. Over the years, the glue came loose, and air started to be sucked into the engine (between the carburetor and intake on the engine). This caused it to run lean and caused a hunting problem because as it leaned out, RPM would change, the governor would respond to correct for this, and the cycle would start over. I also had an old Kohler 14hp where the throttle shaft had worn into the shape of a football where it contacted the carburetor body. The throttle shaft would wobble because it was not I full contact with the carburetor hole. In both cases, I had a hunting issue like you have. I learned the trick to spray carb cleaner at the intake manifold and near the carburetor exit as well as the point where it entered the head. When I did that, engine speed would pick up (because I was adding more fuel and thus making the mixture less lean). Keep in mind "lean" means not enough fuel for the amount of air, and rich means too much fuel for the amount of air. The Carb cleaner check is quick and easy way to check this. If you see no change in behavior, then you don't have an air leak. (also check the throttle shaft for wobble and maybe give a small shot there to see if it is sucking in air). Also make sure the throttle and choke plates are on the shafts tight. A lose plate will wobble and change the amount of air getting in as well.
If you are not drawing in too much air, then it must be getting less fuel than it needs for the air it is getting. This is likely a fuel supply issue (plugged filter; plugged fuel line from the tank to the fuel pump
or (float/needle not working properly) or (internal carburetor orifices blocked). Are you comfortable taking apart the carburetor to clean it out? Another place for leaks is if the float bowl seal is not tight or is damaged.
You can bypass the fuel line and filter from the tank to the carburetor by "gravity" feeding fuel into the carburetor port. I have used an old plastic beverage bottle for a temporary fuel tank for testing. Get a short piece of fuel line, drill a hole in the plastic lid of the plastic bottle a little smaller than the OD of your hose. Then squeeze the tip of the hose about 1/4" to 1/2" into the hole in the lid. Fill the beverage bottle about half-way with good fuel, put the lid on it and connect the other end of the hose to the input on the carburetor. start the engine while holding the bottle upside down (so fuel drains out into the carburetor). If the problem goes away, then you have a plugged line or filter. There may also be a plugged port in the tank. If the problem persists, then you know it is in the carburetor. (assuming you ruled out air leaks and spark issues)
Hope this helps.