Don: because of the symptoms I do suspect some kind of intermittency in the 1394 connection, but the evidence suggests that the problem is not with the STB or the cable. I've tried to orient the cable connections so as to reduce stress on the connectors, but I've also tried a non-Panasonic cable and the problem persists.
From other postings in this Forum (Roger's, I think) I had gotten the impression that the digital heads on a PV-HD1000 were good for something more like 1000-1500 hours rather than for 3000. The first VCR on which I replaced the heads had been purchased used, and I have no idea how many hours of service it had seen. But it was definitely exhibiting the dropout, "green-flashing", and end-of-tape problems so often described here. The head replacement cured those problems.
As for how much use the VCRs get: rather a lot. I'm taping most of the HBO and Showtime movies and timeshifting some network HD. The problematic VCR, the one I'm discussing here, was bought new a year ago and has gotten more use than any of the others. It could certainly have accumulated more than a thousand hours in that time.
Concerning Roger's questions:
1) Tapes made on the misbehaving machine will generally play properly on other machines, yes. (Without anything like the stop/start problem, if that's what you mean.)
2) Yes, the start/stop problem is present regardless of the source of the tape. It happens with tapes recorded on the defective VCR as well as those recorded on others.
3) I believe I've seen the start/stop problem occur at various positions on the tape, but it's been a while since I checked that. (Most playing is done from the beginning, naturally, and once playback has begin successfully it usually continues that way without interruption.)
4) I haven't attempted any wiggling or banging. I've tried removing and replacing the FireWire cable but it didn't affect the problem in any obvious way.
5) No, I don't have a service manual. (Perhaps I should.)
6) The tapes I use for recordings are always new, or have been used at most a few times. Mostly I use Fuji ST-120 S-VHS tapes (originally Don's suggestion), which work well for this application.