I would start with adjusting the brakes again. I've adjusted mine before and they loosened up after a few miles. In reality I imagine the brakes seated into their normal running position. I never had to adjust a third time though.
Next I would go with the star wiring. Mine is still the factory wiring, but some day I will convert to star as it just seems like it would be better.
Also you mentioned leading with the trailer brakes and a Prodigy controller. Are you using the manual lever to lead with the trailer brakes or cranking up the boost. If using the lever, try maxing the boost and you might not have to touch the lever again.
If you are getting an intermittent NC reading I would check your ground. You should have a dedicated ground wire from the trailer back to the tow vehicle. Do not rely on aground through just the trailer ball.
True story, I had a motorcycle trailer with a 4 blade flat wire connector, but the ground wire was not connected to the plug. I pulled the trailer that way for years (teenager) without a known problem. Then one day I was turning a corner at dusk and the trailer hopped a bit through the gutter and I saw the lights all go out and come back on. It took me a second to realize that the coupler had enough slop that as the trailer bounced, the coupler lifted slightly off the ball breaking the ground connection. I added the ground wire to the plug and the problem never occurred again.
to sum my suggestions up:
Set Prodigy to boost level 3. (manual is online or call them for one)
Increase gain on Prodigy.
Adjust brakes again.
Check, repair, or replace all brake and coupler grounds.
Rewire in star pattern and include grounds into this rewire.