The dead speaker was dead for the very excellent reason that one of the voice coil leads was just dangling by one end. It had broken loose somewhere inside the speaker and then pulled free of the speaker cone, leaving an empty hole.
Rather than spend $100 on a new speaker with the closest specs (these are special-design Eminence speaks, and the Sunn don't shine no more), I thought I'd see if I could reconnect the wire. If I fail, I'll be buying a speaker anyway.
First I sliced a big hole in the paper dust cap. It was easy to see where the wire had broken loose from the hardened black adhesive (the hole's at the top). Down near the voice coil I dug up the end of the solid coil lead and pulled it out of the black stuff a bit. The speaker checked OK for continuity between the end of this lead and the other (good) speaker terminal, so I knew the coil itself wasn't toasted.

The braided lead and the solid lead had been clipped together originally. Maybe there's a reason for using a clip instead of solder, but I figured I'd just solder them together and take my chances. I filed as much black junk as I could off the two ends and then poked the braided lead back through the whole and soldered it to the solid lead.
I ordered a couple paper dust caps and a bottle of black speaker goo. The goo came with the cheapest, trashiest brush ever invented, hairs dropping out everywhere. I gooped up the joint as much as possible and plugged up the hole too. The black stuff started setting up in about 5 seconds. It gets rubbery first and then hardens. BTW, you can see the other (good) voice coil lead on the right in its original condition. Apparently nobody worries about the black gunk changing the sound of the speaker much, at least when used on this part of the cone. My goal = an immobile mass of blackness on each side of the joint, hopefully preventing a new break.
I also trimmed the rest of the old dust cap out with a razor blade, leaving only the ring where it's glued to the cone.
Powered by Nasti-Brush TechnologyTM.
Small beer break.
I set one of my dust caps in place to see how it fit. I'm holding the spare. The new caps don't have a flange along the outside the way the original did.
I picked up the cap again and blew duster-can air into the gap between the voice coil and the center of the speaker to get any dust or paper bits out of there. Then I squeezed a thin bead of glue all the way around the old dust cap ring and quickly set one of the new caps on top of it. I had to press down gently to make sure the edge was in contact with the glue bead all the way around.
I didn't want to sit there all day holding the dome down. Problem solved.
Installed! One of these things is not like the others....
It sounds great so far, and all 4 speakers are pushing equally again. The only thing I can check on is the seal around the new dome, and that looks fine so far. If it goes wrong again, I'll be sure to maintain an embarrassed silence about it.
