Bad speakers can degrade from static to no output, so it can be a speaker.
But battery that is dead and acts like a drain on the Power Supply does the same thing. So swap batteries on the T1. The age of that engine is about right for battery failure if it hasn't been changed recently.
I would reload the sound file on the Hudson and see if that fixes it, if no motor lead issue. Just rereading the post so you actually have speed control in revers just can't get full stop? Still can be a wire though. In reverse the White will have full DC voltage and the yellow becomes ground control. If there is low resistance short between yellow and chassis ground it might cause this.
3V processor are becoming hard to come by now. It may be repairable, but since the fet works in fwd, why it doesn't in reverse leads to the main processor which is not repairable.
It can be tested out of the engine, but I would do a reload of the Sound file first. G
