As a general rule I think the motors (usually older motors) wired internally were not intended to be run on 240V. Ihave been running 3ph motors on single phase for years as the 3ph machines are cheaper to buy s/hand due to lack of diy 3ph availablity.
I have also never used a proprietry inverter due to cost considerations, but have sacrificed some torque and used capacitors to give "quasi" 3ph. Whilst this may be frowned upon I have found this to be a good solution on motors up to 3HP. As Ross has decided to use a different motor this is academic, but I mention it in case someone else wants to run a 3ph motor on single phase, provided of course the motor is configured as 240v delta. G.