[Richard]

The issue is the long run of under gauge wire that travels both through the switch and the high/low relay. Halogen lights should be seeing about 13.5 or better at the light with the engine running and the lights on.
http://newellgurus.com/showthread.php?ti...&pid=31285

Whatever you do, please do not retrofit led bulbs into the existing housings. As a guy who worked for an optics company, I beg you not to do this. Use DOT approved lights. Retrofitting usually produces a TON of glare because of the mismatch of the emitter (bulb) and the reflector. Please don’t be THAT GUY with the super bright lights that blind the oncoming traffic.

With as clever and detailed oriented as you are, I would add the relays and put new bulbs in the existing housings. You need clean power to the headlights regardless. If aren’t happy, then find some DOT LED lamp assemblies.