Turns out the solder was only two wires and no actual pigtail. I guess this must have been a different era where someone trimmed out or slid the insulator on one wire, wrapped the other wire around that straight bare segment, then soldered it together and covered it with maybe electrical tape or self-bonding rubber tape. I covered the ends with lever connectors so I didn't have to worry about it shorting.
I just cut it out and used wire nuts. It was barely enough room to trim a little bit of insulator on each wire and then add a pigtail to each pair. I didn't twist the wires, which should make it easier to redo the connection in the future, although I suppose the pigtail can be lengthened with a wire nut. I also had to try again after a used wire nut that I had handy didn't seem to bite well on three 12 AWG wires. A reused wire nut can work, but apparently they grab much better (especially with thicker/more wires) when they're new so I used out a new one. The metal spiral will deform and squish down once it's used.
I was debating whther or not to use a lever connector, but decided to connect with another pair of wire nuts to another pigtail. Even with the wire nuts, I don't think I could cram a GFCI receptacle into that box - even one of the smaller ones. It also has two long pieces of really stiff wire sheath that won't budge.
I'll just need to get the steel GFCI cover and it will be good. I did tape up the sides of the box at about the line terminal height. For whatever reason, Leviton put the line terminals down (with the ground pin down) and close to fully out, but recessed the load terminals about 1/4".
It looks OK. Fortunately it doesn't have to be seen. I will install the steel cover. And the tester doesn't show that the box is grounded.
Thanks for all the suggestions.