My 2 cents:
Sounds like you're so close now to having it fixed, I would think you'd want
to take the last steps. You've narrowed it down to cracked or missing
backplane connector shells. This is definitely why slot one is dead, and my
guess is you also have one shell fractured in slot 3. My recollection is
that these contact tensioning covers are nylon, snap fit into place, and
become yellow and brittle over time. I would try to get replacements from
anyone currently selling Tek parts: Sphere Research, Surplus Sales, Deane
Kidd, plus the couple guys who keep showing up on ebay with new Tek parts. I
can't recollect the names off hand--one is local here in Aloha OR I think and
the other is in Canada. When the latter puts parts up on ebay, he puts up a
couple dozen at a time so you can't miss him. I find them with my daily
search for "Tektronix new". Only if that didn't pan out, would I scrap the
mainframe (unless there is more wrong than I know).
I remember I had a 7704A while at Tek many moons ago and the readout shimmied
a bit on that also (and it was near new at the time). I wonder if that isn't
a normal trait. I also remember having to replace those nylon shells a few
times back then.
Good luck either way,
Don