Thanks everyone for the suggestions. I got rid of the loops on the ground wire and connected them properly in the picture below (the green wires with the blue hat).
I also spent some time at HD with an electrical guy. He helped me understand a little better what was going on. They have junction boxes there, but not very many of them. I am going to check out EWS (Electrical Wholesale Supply?) to find one that will be the correct size. I will put the ballast and all the wiring in that.
Also, to tidy up the wires going to the reflector, I am going to take the little hats (whatever they're called) off and connect the wires using these waterproof butt splices instead. It will allow the wires to run in line and will look nicer. It will also protect against any splash that might get up there.
After that's done, then I can worry about twisting the wires together and making it all look nice. How does that sound, y'all? I'm not a total lost cause, am I?