I am having a very similar problem with a Tekonsha/Prodigy P3. Let me back up just a bit. This past May we were on a 3,900 mile 23 day camping trip to the Outer Banks, SC, Florida, etc. About half way through the trip my P3 display died. However the P3 was still working, sort of. By sort of I mean the P3 had an intermittent Overload No Brakes shortly after I moved it from a 2014 RAM 1500 to my 2017 RAM 1500. Never had any trouble with the P3 in the 2014 RAM and same trailer. Of course I had to buy a new plug-n-play cable for the 2017 RAM. My Minnie Winnie trailer only weighs 4800# loaded and even when the overload occurs the RAM stops it but really needs the help from the P3. Tekonsha swapped out the P3 with the bad display for no charge. Great customer service. The new P3 does exactly the same thing. Because the problem is so intermittent I have never been able to tie it down to hard braking, soft braking, etc. Sometimes I come to a stop with the error on and the moment I release the brake and reapply it the error goes away.
Someone mentioned rewiring in a star pattern meaning that all brakes are in parallel (I think that is what you meant). This would not work well because all brakes need to be in series as they are wired from the factory. I really like the idea of rewiring the brakes on the outside of the axle housings. With terminals attached to the frame it would be really easy to diagnose which brake magnet might be causing the problem by bypassing the individual magnet.
I would really be interested to hear from anyone who has the intermittent problem and how you fixed it.