***UPDATE***
Pulled the output line from the pump, placed some blue paper towels in front of the nozzle and hit start... several times. Plenty of gas flow.
Time has run out on me. Looks like I'm off to Harbor Freight for genny. Always wanted a dedicated one for the homestead anyway.
Unless you have any other thoughts that would take less than 5 minutes' more worth of diagnostics...
Float and needle?
I have photos of those in place... with the set screw holding the horizontal fulcrum pin... and I tested the freedom of movement of the float and needle before a buttoned 'er up, so...
What the heck could cause it to run so smoothly and then surge every 10 seconds or so.
If it were a constant surge, that I could understand. It just seems like it has to be fuel!
