The models with the rheostat are wound different, and provide a little extra field excitation, which the rheostat limits slightly to throttle the field to put the output where you want it. If the genset dosn't have it to begin with, a rheostat would only lower it more...
Some electrolytic filtration capacitance put in circuit right after the bridge rectifyer will increase the output voltage. Electrolytic caps are used for DC filtration, and are NOT used on motors, so you will find them at electronic supply sources. This is pulsed DC voltage at that point(a real ugly waveform) that the capacitance will flatten right out into something resembling actual DC. This capacitance reacts with the inductance in the windings, and the smoother more stable DC input to the field increase the efficiency and generator output voltage. It also cleans up the output waveform a bit. If it were me, before I did anything, I would run down to radioshack and buy the largest bridge rectifyer I could find and take the original one out of circuit. A weak or bad diode in the bridge rectifyer or a bad electrical connection in that circuit could limit your field current and the output voltage.
If the rectifyer isn't the problem, The voltage at the output of the rectifyer is only about 70V peak, so you need around 75V electrolytic caps. I have used 50V ones successfully on my ST-5, as the peaks are very short in duration(average voltage of the signal is below 50V). You probably have an amp or so of field current unloaded, and perhaps as much as an amp additional for each 2KW of electrical load. Based on that, I would start with 1000 Microfarad(uF) per amp of field current. The ones I use are about the size of a D cell battery with two screw terminals on one end, rated at 1200uF each. They work like a battery, and take in the pulsed DC(charge) and discharge slower, averaging the pulses into a very flat waveform. Because they work like batteries, they are polarity conscious, and one terminal will be marked with a + or POS symbol. The caps are installed in parallel which in capacitors adds their capacitance together, much like the AH capacity in batteries is additive when batteries are wired in parallel...