Terminals and tinsels ok, still attached to the cone, and the voice coil seems good, too.
I used acetone to loosen and lift the glue holding the outer ring. Putting the woofer on its back with the outside surround disconnected, my audio test produced no buzzing and no cutting out. I then presume that the problem is the cone rubbing the voice coil.
Following advice given here in AK, and on the Decware.com refoam page, I cut the dust cover around 340 degrees, leaving a connected edge to fold it back out of the way. Then I inserted four shims into the voice coil made from small strips of index cards. The cone now would not go up or down, and the spider was level. I re-glued the outer edge of the foam ring, and it is now drying overnight. Tomorrow morning (Saturday) I will take out the shims, check for rubbing, and lay the woofer on its back for an audio test. If all is well, as I think it will be after the shimming, I will re-glue the flapped dust cover, and let it dry for several hours.
I will report back here, but I suspect that you all have helped me identify and solve the problem. If so, I will break them in for a few hours before I take them to their home. My father-in-law will be very happy to have his Boston Acoustics A-60 pair up'n'runnin' again!
I will let you know. Thanks to all who contributed to this thread!
Sax and Guitar