Happy to report back here that I did solve my problem!
I went out this morning to put the stock halogen bulbs back in, thinking that would solve the problem. It did not.
So, as a final resolve, I removed the headlight/turn signal combination switch for a good clean an re-greasing. It wasn't too bad of a task, and was actually quite fun/interesting to disect and re-assemble. Put the combination switch back in the vehicle and voila! Everything works now. Excited to put the LED headlights back in at the house. I bet they work perfect now.
Solved:
- Headlights back on; full force, no flickering
- Hi-Beams stay on when engaged (don't revert back to low beam)
- Fogs come on; no more relay buzzing.
What happened (I think): When I first test drove the car, I noticed an issue with the lights wanting to flicker. I jiggled the stalk, and they started working just fine. At that point, it was an occasional issue. But, as with all issues, they always get worse. I believe it was a mere coincidence that when I installed the LED lights the headlight switch was just about on it's way "out" of being functional. The connections inside were so badly corroded that it only let a limited amount of voltage to the headlights. However, (again, coincidentally) the LED's take such a low amount of wattage that they actually did fire and function...just not well. As a result, they didn't send a strong enough signal back to the fog relay to tell the fog system that the headlights were on. The fog relay got a half-strength voltage/signal, and rattled like crazy trying to decide what to do (ha!). When I went to install the halogen bulbs today, the voltage issue was much more obvious, as their wasn’t enough voltage to power the needs of the OEM halogen bulbs (even though the LED’s halfway worked on the voltage being sent, which is a testament to their lower than OEM-spec current draw!).
Upon removing the switch, I had melted plastic around the shroud RIGHT by where the headlight contacts are. The contacts (one especially) had old (and now) burnt grease caked on them, and were not allowing for a good contact.
I cleaned everything with a q-tip and alcohol. I hit the stubborn spots/grease with a small flat-head screwdriver, chiseling away the old goo. Once clean, those spots got wiped down with a paper towel, then alcohol wiped and dried.
Once all was clean, motion parts got WD40 treatment. Then all electrical contact points got some grease. I used “Bulb Grease” since it was what I had on hand. I know “Di-Electric” grease is most appropriate, but again, that’s what I had.
OK, so in case anyone else has a similar issue, hopefully all of this can help you.
Thanks to everyone for your input. Looking forward to getting the LED lights back on and seeing what they can REALLY do!