OK, so a minor wiring change.
Again, let's go over the challenges we face.
#1 the mightybord output does not switch a positive signal, it is an FET that grounds. That cannot "drive" any other circuit as it "sinks" current, not sources it.
#2 in order to ensure the FET is fully on, we need a voltage greater than 5V signals produced by the atmega 5V processor outputs. That is why your other controller also uses more FETs, they are not being driven to a full on and lowest resistance state to prevent heating. Paralleling them lowers the total effective on resistance and "shares" the load across multiple devices.
#3 there is an upper limit we can drive the gate voltage with and that's 20V not the 24V. Gate drive voltage as drawn is sourced from the HBP output terminals as drawn. I assumed you used 1 power supply voltage of 12V and now you have a mixed system of 12V and 24V.
What I didn't want to do was modify the mighty board. For a number of reasons, that's not easy and also just not the safest option.
It still can work, we just need to slightly adapt the wiring.
First, BOTH the 12V and 24 V PSUs need the negative output terminals tied together with a single wire. I realize you probably have both connected to ground or earth on the mains inputs but the output negative only must also be bonded between the 2 supplies.
Then the only wire going from the new FET module to the main board will be the smaller screw terminal negative goes to the switched HBP output negative. The smaller screw terminal positive now would run a short wire back to the 12V power supply + terminal. The HBP also has 1 wire that goes to the positive PSU 12V terminal and the other wire from the bed goes to the "B" terminal on the FET. The "G" terminal on the FET is connected to the 12V negative PSU OUTPUT.
Again, the summary of changes is 2 wires.
The 12v and 24V PSUs get a wire added connecting the negatives.
The + labeled small screw terminal no longer connects to the mighty board and instead, connects to the 12V + PSU output.
I'll make a drawing.