Thanks for the photos. I don't know nearly as much about tube drive 10EEs as guys like Russ, but I do know about the WiaD DC Control panel, which is very similar to the one used on square-dial motor/generator (MG) machines. Both panels use the same Cutler-Hammer No. 222 Field-Acceleration (FA) relay.
The two drawings that you
posted appear to be from the 1956 WiaD-drive 10EE manual. Note that those drawings don't match your panel. The panel shown doesn't include the two resistors in the upper-right corner and uses an AP relay with only one one winding, the series winding.
The function of the FA relay is to sense when the armature current is high, as when the spindle is accelerating under load, and put the field to 100% to help the spindle accelerate. In MG drives, the FA relay does this by bypassing the field-weakening rheostat, wired in series with the spindle motor's field. In WiaD drives, the relay interacts with the 6SF5 tube. (Not being a vacuum tube guy, I'm not sure how that part of the circuit works.)
The FA relay used on your panel (and all square-dial) panels have two windings: a series winding and a shunt winding. The series winding connects in series with the spindle motor's armature and directly senses the armature current. The shunt winding is connected in series with the two resistors and wired between E1-2 and F1. E1-2 and F1 are the two sides of the bus that powers the DC panel, among other things and should see a constant voltage. It appears that at some point Monarch switched to an AP relay with only a series winding (which is what your manual shows).
What it looks like to me is that your armature is drawing too much current at low speeds and that's what's triggering the AP relay. If you have access to a clamp-on ammeter that can read DC amps, check the armature current when the machine is operating normally and when the AP relay is acting up. (Make sure you know what you're doing if you're going to attempt that measurement, as lethal voltages are present on the DC panel.) I would also check the armature voltage (DC voltage between A1 and A2) and the voltage between E1-2 and F1. All of the measurements can be made at the terminals at the bottom of the DC panel. Armature current and voltage should not exceed the values on the motor's name plate. E1-2 to F1 should constant at about 115 VDC.
If it turns out that the AP relay has a problem, I have a line on several replacement relays. Don't be in a hurry to replace this drive. It's lasted almost two thirds of a century; fix this problem and it will probably run for decades more.