As it looks like you have managed to remove the old terminal block without damaging the PCB, you might consider fitting a new terminal block. It's a standard size 32A one AFAIR.
I suggest you check the PCB temperature in the vicinity of the soldered joints you have made when the heaters are running at full power.
As Tim says it's a bad idea to do that while powered as you could induce a short between the heater and the thermistor/PT100 that can damage the board.
That said you can change the time a heater will tolerate a fault by using M570:
That sounds feasible. However, I think it's simpler to route everything through the 10-way ribbon cable. If your Duet WiFi PCB is version 1.01 then it already has the transmit, receive and +5V lines connected to the CONN_SD socket. Then all you need to do is to jumper those pins on the back of the PanelDue board from the ribbon cable connector to the 4-pin connector.
Noctua doesn't offer any 24v fans. All of the 24v "quiet" fans that I could see on Amazon in the US are super chunky, and I'm not too confident in picking from digi-key's catalogue.
