Good ideas that I haven't tried. Thanks, I will let everyone know how they work out.
I am using the solenoid electrical connection to supply power to the electric pump and the solenoid. When I was going through the electrical/fuel systems, I tested the solenoid operation and it was ok. Of course that was 2-3 years ago. That probably needs to be investigated also. The 727A has always been quirky after it got old, like me. Anything is possible.
I have always suspected the "compact" part of the 727A description was part of the problem. Most of the fuel system is directly above the muffler. I put in a heat shield above the muffler to no avail.
Full disclosure: I bought the 727A specifically because it was maneuverable and cut a 54" swath. So any "compact" related issues are on me.