UPDATE!
I managed to fix at least one of these issues. I have no idea why this is the
case, but while it appeared that my fuel pump pickup was reaching the
bottom of the tank, it was actually only the far end (from the pump) of the
filter sock drooping down to contact the bottom of the tank. The pickup
tube, itself, was about an inch off of the bottom of the tank!
I modified the fuel pump bracket to make the pump sit about an inch lower, so
that the pickup is now fully on, or at least close to, the bottom of the tank!
I have no idea why the fuel pump was not sitting low enough in the tank. I
can only imagine that the tank or the bracket are not original, or that the
pickup/filter is not correct. The pump is the correct part number from Walbro,
and while the pickup looks correct, it has no part number on it.
In the following (huge!, sorry) picture, you can see there two bends in the
bracket. The higher one originally went out perpedicular to the pump and held
it in place. I bent this down and then bent a portion of it, further down,
back out to hold the pump and then added a hose clamp to assure it stays in
place. Note that the hose clamp is not very tight so as to not tweak the
internals of the rotary pump, but won't back off, since I secured the worm
gear screw on the other side by bending over the unused portion of the
clamp.