I used the putty. Just worked it in there until it was solid.
Another thing to note is the lock washers holding the plastic shroud on the fuel pump assembly. They're easy to break but try to save them if you can. I couldn't find replacements that weren't zinc, which can't go into fuel.
No special solder for me. Just electrical.
One more note: while you do want to heat the socket up enough to bond with the solder, don't overdo it or the solder on the other side might melt.
Thanks for all the advice – I'll let you know how it goes.
This is all hitting at a bad time – the folks I rent my garage from have sold their home, and I need to be out by June 15... And I'm leaving next Friday for France/Germany until June 1... Ugh.