Thought about simply editing my post to Fentress and putting this in there, but figured I'd make a new post so anyone who encounters a similar issue will know to try this.
Before I get to that though, I have to say this really,
really bothered me. I worked on electronics in the Marine Corps and not being able to solve this issue was really bugging me. On top of that my father-in-law is an electrical engineer (along with being a farmer, haha) and when I ran my 'troubleshooting' by him we both came to the conclusion that I'd covered all the steps and the LEDs were likely defective.
Flash forward to late this morning. I asked my father-in-law to come by so that we could wire both LEDs up at the same time. I didn't think it would work. He didn't think it would work. Nothing that I read online indicated that both had to be wired up for it to work correctly, either. But the 'troubleshooter' in me wouldn't let it go and that was the only thing I hadn't tried.....
...and they still didn't work. Bummed, we were just about to unhook the LEDs and reinstall the halogens when a thought came over me: what if the plug for the LEDs are wired backwards? We'd be hooking them up with the little 'nipple' that the 'fingers' on the plug grab on to the proper way (so that it locks.) I decided to flip my plug around to where the nipple was on the back side of the fingers. Success! Did it to my father-in-laws side and we now had working LED high beams. There is a rubber plug that fits very tightly inside the plug side of the LED that should keep it wired up correctly, but since the nipple and fingers are on opposite sides it isn't 'locked' like it should be. I didn't do it today (yet), but I will use electrical tape to make sure they don't wiggle apart (but, again, that rubber boot keeps things very tight, anyway.
TL;DR
If your LEDs don't work even after wiring them up, try flipping the plug around. It was kind of a last ditch effort on my part and thankfully that was the issue.