I also purchased the 3 phase version of the 1340GT, for the reason it saves you the cost/installation of a new 3 phase motor. Changing the motor to a true vector rated 3 phase motor (such as the Marathon BlackMax/BlueMax series), does afford you full torque down to 0 RPM, and full horsepower rating from ~1750 RPM up to ~3500 RPM for something like the Y526 or Y551 models. So much wider working range, and no low speed cooling limitations, but they are costly and not sure if they would fit.
The wiring for this version lathe is set up for a 3 phase connection, availability from the power company it is not something you would see in a residential setting. So one cannot simply connect a VFD and run the machine without wiring modifications, but one could use an electronic or rotary 3 phase converter. A VFD in a vector mode, gives very smooth power delivery over a broad RPM range, plus the advantages of an electronic brake and to some degree motor feedback operation to the VFD. Conversion of the 3 phase lathe/motor to VFD operation is not complicated, but one needs some basic knowledge of electricity and wiring of VFDs. One should use shielded wiring to the VFD controls and for wiring between the VFD and the 3 phase motor. There are also a number of tweaking (programming) variables with the VFD set-up, some are a bit more complex than others. I have opted for relay controls of the VFD signals, which affords some additional controls of other devices and interlocks for additional safety.
Mark