Tim, After having worked on a ba-zillion gas
motors in my lifetime there are only three systems to look at. Mechanical, fuel and fire. Now if the engine hasn't been using oil to any extent between seasons and the compression is ok you can assume the mechanical is ok. Compression can be checked with a compression gauge, with the spark plugs out, either using the electrical starter or hand cranking. As long as the 2 cyls are within 10# of each other it is ok. If the engine runs ok for awhile like you say and then abruptly misses then I don't think there is any mechanical problem.Now electrical. #1. Start out with new spark plugs of the type suggested by the manufacture. I only use NGK or ND plugs in everything I build including the "race engines" I build for myself and others. They are Japanese plugs and I've never has misfire problems with them under severe loads. Set the gap, anti-seize (lightly)the threads and install. Check the ohms resistance of the spark plug wires to be sure they are good. Very often people pull wires off wrongly and damage the inner core of the wire which leads to misfiring under load. The resistance should be under 5,000 ohms. If not, replace the wires.Now fuel, With the engine warm and idling, adjust the idle air screw for best idle. (not the idle speed linkage adjustment) If after adjusting this mixture screw if the idle has risen too high then adjust the linkage screw to lower the idle. If this doesn't remove the problem you can try to find someone knowledgable on small engine fuel systems if you don't feel comfortable doing this, or, get a Honda service manual, usually under $20 from Honda. These are excellent books and can help the earliest of beginners walk thru a Honda engine. Write back if I can help further.RayS/V Speedy