Is the FET gate floating? Maybe try adding a pull down/up resistor as a sanity check. I have no Duet experience. Based on what you are saying, I would troubleshoot that hardware first. Cut the trace and see if the gate signal is going off as expected… things like that.
Removing the SD card shows whether there is a burned or shorted connection somewhere, but does not show if a gate is staying high after it is triggered. HCT logic is translating CMOS threshold voltages on the input to TTL levels at the output. Still while the window of where bit logic high and low are specified, the actual logic zero voltage is relatively high. You also have to remember that all chip manufacturers have an error rate distribution curve and send bad parts or parts that are right on the edge of acceptable. It is quite possible that you happened to get a FET with a low gate threshold voltage and a logic gate with abnormally high logic zero threshold. I would just tack on a through hole resistor between gate and source similar to how Fan 2 MOSFET control is configured and see if that solves the issue.
I’m not effectively able to help with the software, so this may still be a red herring, but I do not think removing the SD card effectively addresses the question of whether the gate is driven low correctly.