Since MTH does not publish schematics, perhaps the following might help. The generic 2-FET with relay DC motor controller is quite simple. There are other parts of course for current limiting, clamping, etc. but the basic idea is an SPDT relay applies positive voltage to one of the motor leads. Then one of two transistors is pulsed on to "ground" the other motor lead. If your relay is indeed toggling properly, then either the FET is "open" and not turning on, or the logic circuitry is not providing the buffered control pulses from the head engine tether to turn on the FET.
The red lines show the current path for each direction showing how the relay and FETs work together to reverse the polarity of the current through the motor.
I'd think at this point, to go further you need to power up the system and make measurements which I realize can be logistically difficult. I suppose you could disconnect the head-engines motor so that nothing moves when you command the head-engine forward or backward. Then you can look at the slave FETs to see if they get control voltage slaved to the head direction. The Vgs voltage pulses should go from 0V to probably 5V since you have logic chips driving them.
As G says, if a FET is "shorted" on, then something would happen in at least one of the directions. If the FET is "open" off, then BOTH would have to have failed for nothing to happen in either direction. I'm starting to like the logic circuit. Perhaps Matt can step in and identify the exact logic component he changed as it sounds like his symptoms were identical.