You mentioned upgrading to a heavy duty wiring harness. How is this harness wired and what does it include? Is it just new H4 sockets with heavy wire or does it utilize a relay?
I know that tracking down the problem and fixing it (then upgrading anyway) would be the ideal solution, but that can be time consuming and darn near impossible so if there isn't a short, and everything is fused for safety then I would recommend wiring the harness with a relay such that it uses the original headlight harness strictly as a signal for a relay and run power to the relay straight off the battery and then from the relay to the headlights. This way a voltage drop in the OEM headlight harness won't affect your light output (as long as the drop doesn't fall below critical voltage of the relay).
Wiring the lights this way will decrease voltage drop even in a system w/o problems and possibly increase light output.
[source: Hella KG Hueck AG, Germany]:
When operating voltage drops to 95 percent (12.825v), headlamp bulbs produce only 83 percent of their rated light output. When voltage drops to 90 percent (12.15v), bulb output is only 67 percent of what it should be. And when voltage drops to 85 percent (11.475v), bulb output is a paltry 53 percent of normal!
If your upgraded wiring harness included a relay and you have it wired this way (using OEM wiring for signal only) then I can't explain your symptoms. Short somewhere? Bad relay?
Hope this helps.
-Heikki