Seems I've yet again posed a mystery question.
Anyway ... the washer not taking coins had a piece of the mechanism dislodged, jamming the slide. Forced the slide in/out with coins, the piece of question came out atop the slide, slightly mangled. Straightened and put it back in place. Not sure how it happened considering where the piece goes, although the owner and her handyman tried to fix something-or-other on it and may lost track of the piece's proper position.
The other washer leaving the clothes wet ... no apparent problem. Coupler good, agitates (dogs are bad), neutral-drains, spins (sufficient torque), brakes, inlet valves don't seep (unless they do on-site).
The dryer not taking coins remains to-do.
JHC, they're gnasty. Huge sympathy for folks who must use coin-op laundry.
Situation proved to be one of those degrees-of-separation things. The RV Park handyman also does yardwork for my parents (which is how I got involved). The owner was a classmate of my mother's.