Well, the speaker is repaired. Tapping with hammer and screwdriver worked, but for the wrong reason. The brass thingy is just a bushing that grips the aluminum cone tightly. It may be screwed into the cast iron base, or it may just be driven in, but there's no need to unscrew it. My tapping with the screwdriver just loosened it and I could then pull off the base.
The most effective way to remove the base is probably just to tap it off with a rubber mallet. Then remove the circlip and wiggle off the cone. Take out the three screws and tighten up the RCA. I didn't even need to re-solder the center conductor. The loud 'BLAHHHHHHHHT" was just because the RCA was so loose that it lost ground contact. It all works just like the YouTube says. For those who wanted more pictures:
Here is the view of the base from below, fully assembled.
And here are the parts disassembled:
What you would do next is to tap the base off by holding the cone and tapping the base with a rubber mallet, or perhaps holding the base and tapping on the threaded shaft with a rubber mallet.
