I forgot you have LEDs. I thought the A3 jumper was a metal clip? I thought I saw a pic somewhere. As for the wire, are you sure it's making good contact? Does it get warm at all?
As a test, reinstall the halogens and see if the lows dim with the highs on as well.
Just a WAG, but I am thinking that the jumper takes the voltage that supposed to supply the highs and shunts some off to the lows as well to get both to turn on. If that jumper is too thin, not enough voltage will make to the lows, hence the dim main beam with high on. Since the high portion of the circuit is intact, it operates normally.
A set of relays, where the car's wiring only carries low-load current to trip the relay (rather than power the bulbs) would certainly fix it. I installed a headlight relay on my Vanagon, and the additional brightness was noticeable. Here's an
Amazon link to a relay kit (won't plug into your headlights, just an example). It has a good schematic in the pics of how it's wired in. If you find a kit made for your car/headlight type, it's basically plug-n-play.