How can I bend wire that is too thick to manage easily?
I doubt that it's #10, but even #12 can seem like a pretty thick wire when you're, even casually, used to #14.

I'm surprised your pump receptacle doesn't have clamps instead of screws. Is it a 20 amp, twist lock, single receptacle?

Without using force make sure the device screws are completely backed out, but don't remove them. Strip off about 1” of insulation to get a good size hook. As you're bending it, stop short of a full hook to more of a “U” shape. Put the wire under the screw and complete the hook with needle nose or diagonal pliers, the end of wire strippers whatever works before tightening the screw. Subtle bends and angles can make all the difference getting the wire under the screw.