The rectification is slightly different than normal. Instead of flipping the neg. AC wave like with a bridge rectifier, it just skips using it using only a diode to block the neg. wave; so it's "half wave". The now pulsing ac pos. wave and a pulsed DC are are basically the same thing as far as a motor can tell.
If you do scrap the Tmcc(?*) a bridge rectifier would work. You could also place a diode to the motor to board lead to replace the board. This is half wave also. Which way the diode faces would determine dirrection of the motor.
I think a call to talk to Lionel might be in order. I couldn't access the site, likely due to the parts sale activity overloading the system. I couldn't find reference to the number elsewhere either; not a single return when I searched.
*With the intro of LC, LC+ "reciever" vs Tmcc or other term also has me wondering what's there. I was hoping listing the board would draw in GunRunnerJohn or someone else more intimately familiar with it.