Thanks all .. I hauled the boat and discovered that what I thought was a loose prop was actually loose anodes. I have the Volvo
two-part anodes, that circle the shaft, and are connected by two allen bolts top and bottom, with said bolts passing through machined holes on the backside of the transmission
(sail drive) ... it turns out someone in a yard or the factory had machined out those machined holes so that they were open to the rear (probably to accommodate a close-but-no-cigar one-piece anode setup).
Thus, the anodes could slip back, and made it appear as if the prop was sliding.
As others have noted on other threads (see above posting), these props have a setup like this: prop around splined shaft; plastic washer; threaded cone; allen bolt that fits into cone. To deal short term with slipping anodes, I tapped two s/s metal screws into anode, and then used spectra line to manually pull the anodes forward against the sail drive. This is temporary, since I only ahd a day on the slipway; permanent repair will require replacing the backside of the saildrive with one whose machined pass-through holes are intact (as by design).
I replaced washer/cone/bolt after greasing splined shaft, but given others' losses, will be checking frequently. I checked other shaft, and replaced using RED permatex -- hope I can get it off when I need to!