The SOLE way to utilize 180 degree opposed phases in a 4-wire generator (240 volt) is to use a transformer. 98% efficiency. Changing 3 phase to single phase 240 volts by using a Scott connection (equal 3 phase loading).
Apparently SOME HF generators are reconnectable. 240 to 120. Some ONAN generators came from the factory connected for 65 amperes @ 120vac. My expensive 5500 Yamaha diesel genset was not reconnectable.
Make certain what ever you buy is compatible with your model number and serial number HF generator. If it isn't it's transformer time.
Hint: Many higher powered generators use a PRIMARY exciter to initiate SECONDARY exciter voltage via a dedicated rotor and stator. The seondary exciter amplifies this into the big field winding within the big rotor and the product is dispensed via the secondary stator.