The "drill pump" probably requires priming and a constant supply
of water at its input. Likely not a good choice for what you are
trying to do. The shop vac hooked up to blow air into the pipe
has a far batter chance of drying things than hooking it up to
pull the water out. Of course, that is not the solution to your
problem.
The weak points in your setup, aside from any defects, are at the
outlets at 125' and at 40'. Open them up, clean any dirt/gunk in
the j boxes and _replace_ whatever receptacles are there. Next,
replace the GFCI. Receptacles outdoors and in unheated outbuildings
collect condensation, spiderwebs, dirt etc. A GFCI that has tripped
multiple times may well have burned contacts. So, since you have
to invest time for diagnosis anyway, you might as well replace the
devices you need to remove for inspection/cleaning and the GFCI
(because of the multiple trips). NOW you can start troubleshooting
if you haven't fixed the problem. You DO NOT want to go through
all the effort of pulling new UF cables, digging trenches, replacing
conduit etc only to discover that all you needed to do was spend
$20 and replace two receptacles plus a GFCI.
Wetness in the conduit is not causing the trip alone, and it could
be normal condensation. Of course, if rain water is getting into
the conduit, that's not normal, but it still isn't the sole cause
of the problem. The conductors still have to come into contact with
the water, so one or more of the conductors insulation has to be
compromised somewhere, too. If you have eliminated the other
possibilities, you could try pulling new UF cable in the existing
conduit. If you _know_ rainwater is getting into the conduit
you've got to fix whatever is causing that - which might mean
a lot of digging to run new conduit.
I'm working hard to get you to spend the ~20 bucks for the
receptacles and GFCI - can you tell?
Ed