I suspect I might have a cheap aftermarket piston. Where can I purchase a genuine one? Are there some trusted sources of better quality parts? Regarding the teflon buttons, they would have two diameters. The small diameter would press into the hole in the wrist pin. The larger would be slightly smaller than the wrist pin OD. The head would be rounded. The overall length of the wrist pins and two button heads would trap the wrist pin in the piston. My only concern is temperature.

The EY28 is a good engine, as are all of the old Wisconsin and Subaru Robins. Being a flat head is OK, just somewhat less efficient than an OHV or OHC engine. Your EY28 produces 7.5hp from 280cc, the current EH25 OHV produces 8.5hp from 250cc. The OHV also uses about 20% less fuel. More importantly to Robin/Wisconsin, the old flat heads are not as clean emissions-wise, and can no longer be certified. That's why all of the engine makers have pretty much replaced flat heads with OHV construction, especially in California where CARB standards are even more stringent than EPA. The type of ignition is more important to me. The EY28 came fitted with both electronic and the older breaker-point ignitions. The electronic is almost idiot proof, unless the coil fails. If the electronic fails, it easy but expensive to replace. Breaker points, however are a maintenance item. The need to be cleaned and re-gapped periodically, and are located under the flywheel, which makes it a bigger job. If engine is equipped with electronic (transistorized), forget everything I said. Your regular small engine mechanic should be fine, provided he's competent. I'd pull down the manuals from Subaru (Parts, Service, and Operating) so he has something for reference. I'd also chase the internet to see who handles parts. While things are much better now that Subaru is directly involved, parts are still more expensive and harder to find than Briggs, Honda, or Kohler. No harm trying to light it up, as long as oil is good. Carburetor may be gummed up from sitting, particularly if not stored properly. You may have to disassemble and boil everything out. Check for ignition, then squirt a little gas down the air horn and see if it lights. Then put some gas in tank, and see if it will run. If not, you or your mechanic will probably have to go through the carb.

Sounds like the carb is leaking fuel into the engine while it is stored between uses. The reluctance to crank initially may be due to the cylinder being hydrolocked with gasoline. After enough attempts by you with using the starter, the fuel slug in the cylinder is expelled, but the engine is flooded so it requires extra cranking to clear out enough fuel so combustion can begin. Then comes the big puff of white smoke as the fuel and residual junk in the muffler burn off. You need to add an inline fuel shut off valve to the fuel hose between the fuel filter and the tank. Turn the valve off every time you stop the engine. The needle valve in the carb is leaking fuel is why the problem occurs. You can fix the carb if you like but you must add an inline fuel shutoff valve and close it except when the engine is running. You also need to change your engine oil and oil filter (if it has one) before you operate this engine again. If your carb has been drowning the engine when parked, there is gasoline diluting the oil and that will spell engine failure.

Hmmm ... May 3 was a while back already. Just in case another person reads this, small engines tend to have a very fine mesh fuel screen in the tiny carburator. This tiny screen is the cause of many of the symptoms you speak of, and not easily removed and cleaned without damages. Keep in mind we are talking about a tiny carburator system most of us cannot inspect without a magnifier and "young" eyes. As to why the sparkplug is always replaced; old habit that is worth a few bucks to the mechanic. Besides, they are kind of cheap normally and avoid a lot of issues, or problems that might develop about 10 minutes after you get the machine home. The mechanic is thinking; Why take the chance with the old one? In any case, if you are serious about wanting to learn all you can about small engines, you want to give the local Voc Ed (now called Tech Centers) class/shop some serious thought. Normally the instructor has a lot of years of experience behind him or her when one speaks with the golden tongue for only a few coins of the empire from your pocket. If an adult, you might want to try out the night class for adults, and see if more training is desired later or not. One advantage most adult classes have over the day classes for high school students is you are required (more or less) to bring something in to work on, but the shop instructor can help with this also. You will be surprised how much you will learn without realizing you did. Needless to say the instruction pays for itself as a few years and projects pass successfully towards "repaired" by your hands.