Disconnecting those items from the engine quickly proved it was the engine that was locked. Bummer. This little Honda may have cut her last blade.
With nothing to lose, we pulled the head and took a look. Although covered with tar-like oil, the valve train looked ok. The piston was stuck almost at TDC (Top Dead Center), so we couldn't see the cylinder walls. After applying a big dose of acetone and Automatic Transmission Fluid (the hot ticket for penetrating oil applications), and considerable muscle, the piston broke free and would turn by hand. More oil and more turns revealed no untoward noises and the cylinder walls did not show any scars.
She blew a little smoke at first but ran like a top!
Next up was the transmission, which was stuck in high gear. After removal from the mower (which requires removing everything connected to the rear wheels) it was disassembled and cleaned. Inspection showed normal wear but nothing broken, so she got a full load of gear oil and went back together with no leaks (to my complete amazement).
Back in the mower, with the control cables adjusted to spec, the trans shifted like a dream and the little Honda that almost went to the dump is back home and cutting grass like like a champ. Yes, she smokes a little on start-up...but heck...she's 30 years old. I think that's allowed.