Hi NeoMoses
Yes, you can run the frequency as high as you dare
There are the usual mechanical hazards of running a motor at an rpm higher than it was balanced for, of course, and this includes the rest of the drive train on the mill head, too.
Normally, there should not be too much trouble up to the 3600 rpm, since many motors are built for that speed. The quality of the motor's insulation has to be good, as frequency spikes can stress the insulation, and cause an eventual motor burnout.
For single phase in, 3 phase out, you need to buy a Variable Frequency Drive that is approximately double the hp of what you would need if you had 3 phase input.
I've retrofitted VFD's to various machines without problem. It is really nice to have the variable speed control available for your cnc to command.
Have you checked Ebay for used mills? There are some real bargains there, if you have the means to do some retrofitting and repair.