Some "clever" person has buggered up your Lincoln's electrical system:
1) there is no Voltage Regulator- the box on the inside of the firewall is a Circuit Breaker for the car's internal wiring systwm
2) generator 3rd brush should have a temperature activated switch which inserts a resistance into the field circuit, reducing output current by half. This an early form of control before the application of voltage regulator systems to cars in 1930s
3) there should Not be a solenoid on the starter. The starter gears are intended to be moved into mesh with the starter pinion and toe flywheel mechanically, by a small foot pedal near the throttle pedal. The generator field is connected to the ignition switch, so the generator turns slowly as a motor when ignition is turned on.
The setup you have apparently works, but the original system is simple and effective. t might work to install a simple .6 volt regulator in the generator field circuit.
Get copies of LOC published Model L service books. The starter generator system is thoroughly covered there. There are also some Forum posts on this topic.
Good Luck!