Constant power and electric motors doesn't exist, unless you introduce gearing, as you can't cheat the laws of physics.

Options are either a three phase motor with VFD, or go all out with a servo.

I'd probably go for around a 1HP 4 pole motor, gear it so at rated speed the spindle is running at 500 (about 3:1 ratio), then overspeed the motor via the VFD to get the desired 1000rpm (where you do actually enter a constant power zone of the motor, as torque starts to drop of above the rated speed).