Some results, and a learning experience.
Nothing I tried had any effect whatsoever. A friend suggested the one thing I hadn't checked, which was using an ohmmeter on the antenna housing itself.
The way the housing is constructed is that the pigtail that plugs into the wire to the front, is mounted to the side of the aluminum tube that the mast sits in near the top . Somehow internally there's some barrier between the mast and the tube so it's not grounded; there has to be some insulation between the car body and the mast, but with some contact between the top of the tube, the brass threaded part, and the pigtail. This is why the sleeve is important, the chromed sleeve that acts as a top stop for the antenna, and what may be the problem with others having bad reception. This sleeve can get really dirty and gunked up with lube, and thus interfering with reception. It appears that the sleeve makes/assists with contact between the mast and the pigtail. I think that's why most sleeves have two slots thus making a sort of 'finger' that can press against the side of the mast.
But in any case, when my mast was broken off this somehow damaged the housing internally so that there was no contact between the mast and the pigtail.
My mech gave me a housing out of a 940 that appeared similar; turned out to be the same form factor and wiring, different lower mount to body but easily changed, so I put it in, motor worked, but no up and down of mast. Turned out that a little plastic gear internally was broken. The motor assembly was mostly the same so I replaced the gear with the one out of my old one. The old gears were in better shape than the 940 but the big takeup gear is different in how it activates, that one is not interchangeable, so I left a mix of gears in, checked by hand that things were turning ok, and all works fine.
The faq says that when putting in a mast, that the teeth have to point straight forward. This is the case with some but the lower motor assembly mount in my car and some others make the angle of the takeup reel 45 degrees to the right. Also, putting in the mast can be very difficult. There's some sort of interference where the aluminum tube joins the motor assembly, and repeated poking with the plastic lead aimed carefully got nowhere. I found that turning the lead 180 degrees made it easier to get past that interference, and then turn the mast/lead to the right direction.
I hope this makes sense.