I will answer this myself because after 2 weeks of working on and off on the problem very deeply, I solved it. As suspected, it was a very simple problem that manifested as complex (as they so often do). I went deeply into every component in a process of elimination, including timer disassembly under a microscope (no kidding).
The problem was no SUSTAINING power to run windings in the motor. A number of connectors on the timer were low instead of high, having only inducted current creating voltages and no full line voltage. Tricky voltages like 20 to 60, not just 4 or 6 or something that low, making one wonder how the heck was that possible?
Complicating matters was this machine is a 3-speed washer with 'Whirlpool gold, super capacity plus (thus the S in the model number), 27 cycles… catalyst cleaning action (thus the X in the model number), 6 speed combinations, etc, blah blah. That means a complex time and a gaggle of wires.
Another complication was I’m not sure I ever pegged the right model number, GSX9750P It was very close, if not right. G = Gold, S = super capacity plus, X = catalyst cleaning action, and P = model introduction year 2003. The Whirlpool model and serial was on a paper sticker instead of a plate and I stupidly blew that away with the pressure washer back when I first bought the machine. Not just blown off, but obliterated. Also, the wiring schematic was left out before I bought it. I did find schematic 3955342, which was close but not my model. It helped a lot in diagnosis.
The major complication, perhaps, is that I am not an experience washer repair guy. I had to learn that a lot of wires go from the timer to other things and back, including down to the motor and back. And depending on timer position and fabric select switch settings (controlling motor speed settings), what the many wires are doing changes.
One critical circuit goes from the timer to the motor and passes though the start switch and returns to the timer, powering a number of downstream things. That depends on start switch setting, whether down or up depending on the centrifugal start mechanism (the click when the motor slows down).
The critical circuit powers the run motor windings… all three of them. The orange with blue-stripe wire (OR-BU) sends power down to the motor when the timer enables it. After the start winding spins the motor up enough to move the start switch to the run position, OR-BU power is routed through a switch contact back up to to the timer via the blue with orange-stripe wire (BU-OR) which powers up some reed switches in the timer and terminals on the fabric select switch. Among other things, this powers up the solid blue wire which sends power to the high-speed winding down in the motor such that the motor doesn’t slow back down and cycle again into start mode.
The entire problem was the copper wires having burned in half in a tiny gap right at the Molex terminal blade at the motor on the blue with orange-stripe wire (BU-OR). This burn through was not visible, and the gap was so small you could not feel it easily. I found it finally by tracing the complex power circuits from the wall cord to the motor, which of course took a few trips between the timer and the motor. This was from my inexperience, as I should have gone the other direction with the diagnosis.
Why did I not give up on this washer? Because it is really cherry! It’s like a 2004 car you love with only 30,000 miles and is gorgeous except for one tiny wiring error that turns it into immovable material.
I have my washer back!
I hope this will turn up in a search and help someone else similarly frustrated by the lack of information available. Lots of videos and text on the low-hanging fruit of problems, but very very little at this level!