I don't understand why their TX12 can't start a 3 hp motor. 12,000 watts is about 5 times the running wattage of your 3 HP motor. But what really matters is the current draw when starting. Depending on the motor and the mechanical load on the motor when it starts the starting current can be more, much more, than 5 times the running current. I think Baumalight is just trying to cover their butt because they don't know what the starting current of your motor is going to be.
Anyway, if you have already bought the generator all is not lost. Furthermore, if you haven't bought it but really want it or something similar you can still do so. What you need is a soft starter. Even though you can build one yourself I have a sneaking suspicion that you would rather not. So, for your size of motor, a soft starter can be had for less than 150 frog pelts, AKA greenbacks. For example check out this link:
ATS01N112FT | Altistart 01 Soft Start (ATS01), for Asynchronous Motor, 12A, 110-480V, 1.5-7.5 HP, 1.5-5.5 kW, Single-phase, Integrated Bypass, w/Heat Sink Pack of 1 | Square D by Schneider Electric . $136.90 for a soft starter that can handle your 3 HP well pump while at the same time protecting your Baumalight generator. Of course you should ask Baumalight if using a soft starter is OK but it should be. After all what really matters is what the load is that the generator sees.
Cheers,
Eric