Well, I finally got some time to throw one of the huge clamps into the mix.
Many pics to come.
This time, I used copper wire (Romex) to avoid the anode wire disintegrating. Copper wire to the anode worked fine...but, to my surprise, when I went to un-wrap it, a piece did actually break off. Crazy. At least it lasted through the process instead of disintegrating half way through.
I used a long section of gutter, like
@KazooBR suggested. It was difficult, because it wanted to twist and bend. I ended up setting it on top of a ladder outside, and cable tying it to posts to keep it holding its shape. That worked, eventually.
The process worked perfectly again. I spent a (long) while with a wire brush and Simple Green after removing the black crap that accumulated during the process, and a short time with a wire wheel. Then I coated the entire thing with WD-40.
Pic 1: The basic setup. See battery charger protected from rain and long Romex cable. Gutter trough on left hand side, on top of ladder, cable-tied to fence so it won't twist and bend. Clamp cathode and rebar anode in gutter trough connected to the Romex wires, which are connected to the battery charger.
Pic 2: Close up of attachment. It was tight in there, it barely fit. I used a long piece of rebar as the anode and put some yellow plastic between it and the clamp so they wouldn't touch.
Pic 3: Massive fizzy action after less than 1 minute.
Pic 4: Massive sludge on top after 1 hour.
Pic 5: A literal 1/8" of solid rust that was left on the bottom of the container after I took the part out