Wow, you're treating Lionel's universal series wound motor like a prototype traction motor. Traction motors used in locomotives are DC universal motors are very similar in construction and operation to Lionel's motor. From what you describe is separate excitation of the armature and field rather than having the armature and field windings in series.
Does the field winding rely on the resistance of the series circuit from the armature to reduce voltage to the field, so am I applying too much power to the field with it wired directly to the pickups through the bridge? I thought the bridge would provide a bit of voltage reduction.
Yes.
You could wire the motor in series from the PS1 board. Often the motor leads are red and black, but it looks like yellow and white from the PS1 board in your picture. For example, you can attach the yellow wire from the board to the left brush holder. Then run a wire from the right brush holder to the center lug which the field winding also attaches. Then the other side of the field wire will attach to the white wire. In this case, the motor will be wired in series and operate off of DC fed from the PS1 board. Problem is that the motor will not reverse.
I think the easiest way to have the motor reverse is to wire only the armature into the PS1 board. That way the PS1 board will change polarity fed to the armature. You would have a separate rectifier for the field. You would wire the rectifier to the track which will feed the AC from the track to the rectifier. Then you would wire the field to the rectifier which will feed DC to the field. Polarity to the field is fixed while polarity to the armature can be reversed thus allowing the armature to spin in both directions depending upon the polarity fed to the armature. The problem is that you do not need 18 V to the field. You probably only need 6 V or so to the field so you will need to find a way to drop the voltage down from the track to the field winding. You could put a resistor into series with the field but that may produce a lot of heat at the resistor. Another issue that even when the motor is "off" the field winding is still being powered.
Cool project.