If you buy a new motor, get one that is rated to be suitable for VFD service. I think this implies that the motor can handle 120Hz, which would make a 1725 rpm motor run at 3450. Running at a higher rpm than that may require more accurate rotor balancing and a modified cooling fan that won't explode. Quite often a 1725 rpm motor has a quite beefy fan, with large fins, and it gets quite noisy at high rpm. Centrifugal force on those large fins may cause them to break off after fatigue occurs.
At the lower end of rpm, if the motor is working hard, it will not be properly cooled at very low rpm if run there for extended periods. This may not seem to be an immediate problem in your search for more speed. However, the motor can be used down to quite low frequencies, until it starts to power out. This might be down around 5 to 10Hz or so, if using a vectorless VFD.
If you are trying to get more spindle rpm than 3450, you might be as far ahead to use a mechanical speed increase, via belts and pulleys, to get the spindle rpm up in the range where you want it. This will allow you to cycle your VFD in a reasonable range to preempt the purchase of an ultra spec motor.