Bearing adjustment, SPD pedal

For Back To School, I gave my purposely crummy school bike the bi-annual
once-over inspection and noticed that one of the PD-M505 pedals was
feeling pretty loose on its bearings so I took it apart. I popped off
the plastic end cover and exposed a 10mm stopnut. It was on pretty
tight, and I had to clamp the pedal in the vice and use a 10-inch socket
wrench handle to get it off.

Under the stopnut is the bearing cone that accepts a 13mm wrench -- or
it would, but all of my 13mm sockets are too fat to get in there.
Anyway, the cone turned off with a little screwdriver poking and I took
everything apart and gave it all a cleaning.

Now I'm trying to figure out how to assemble it properly. The socket
used to tighten the stopnut fills the opening so that I can't grab the
bearing cone and prevent it from over-tightening when I tighten the
stopnut. What's the trick here?

-- mike elliott, on a Labor Day weekend with (clearly) nothing better to do.