I agree with you in the idea that this is a beautiful gen set and it has no sense to replace the whole "generator head".
A generator set consist in two big parts: The engine and the generator (head). If the engine fails, you don't replace it, you repair it. The same is with the generator.
A generator head has three big parts: Stator, rotor and the excitation components
The stator, as its name says, is the component that does not move or turns. It has two components: The Iron core, who conducts the magnetic flux in a low resistance magnetic circuit or path and the windings (copper or aluminium wire), where the alternating magnetic flux inducts a voltage proportional to the number of the wire turns and the strength of the magnetic field generated by the rotor.
The rotor is the element that generates a magnetic field in a rotating iron core magnetized by a pair or pairs of wire coils. These coils are fed electrically thru a pair of rings and carbon brushes (brushed) or by inducting magnetically an alternating voltage in the rotor and then rectifying it to feed the coils (brushless).
The excitation circuit receives part of the voltage induced in the stator and "administrates" a current more or less intense, controlling the intensity of the magnetic field in the rotor and this controlling the voltage inducted in the stator. This function is controlled by the AVR (automatic voltage regulator) or by a less sophisticated circuit
Due to the load variations from zero to full, the current circulating in the stator varies too, producing a loss in the output voltage, this loss is detected by a sensor circuit in the AVR, which compares a fraction of the output voltage with a fixed voltage (reference voltage) developed inside the AVR and gives an "error signal" that is amplified and sent to the rotor to correct the error. This AVR action is done continuously to maintain a stable output voltage.
In this point I want to mark a difference: Voltage is a potencial or electrical difference BETWEEN TWO POINTS.
Current is the electrons flow, pushed by a voltage, thru a closed path. Voltage may be present without current, current needs a voltage to circulate.
With this knowledge, I can explain certain tests that can be done by yourself, taking all the safety actions to prevent accidents.
FIRST: Check all the possible connectors, in the breakers, in the AVR, the outlets, brushes etc etc and after reseting them, try starting the engine. If it still fails proceed with the following steps.
With the engine off check for continuity each of the two ac outlets with the circuit breakers closed (On), both must be near zero ohms. A very high resistance in any of the outlets indicates an open circuit; it may be a failing connector contact, a failing circuit breaker or (rare) an open coil in the stator. This last condition will avoid the voltage presence in ONE of the outlets (if it is a 120-240 genset).
A short circuit in the stator generates an internal very high current that will overload the engine in such a way that it will stop or will run at low RPMs in an abnormal way with smoke in the generator head.
A loss in the excitation will prevent the creation of the rotating magnetic field and without a magnetic field in the stator, there are not a voltage inducted in the stator coils.
To start generating, it is necessary an initial magnetic field. The rotor iron core maintains a residual magnetism, enough to induct a very little voltage in the stator windings, this voltage is sent to the AVR, then to the brushes and to the rotor coils, increasing the magnetic field up to reach the desired output voltage.
If this genset is a brushed type, the brushes are the weak point, they have a limited life and if one of them fails, there will not be voltage in the outlets. The brushes are located in the opposite side of the engine. Always there are covers to reach such brushes. Check for continuity between both brushes with wires from the AVR disconnected. A high resistance means bad brushes or an open condition in the rotor.
A probable failure cause is a fail in the AVR. This is the last point to revise and the only way to test by yourself is replacing it.
Sorry for the long explanation but if not for you,it may be useful for other readers.
Hope to be helpful.