A VFD with integrated support for encoder feedback would be a very nice option indeed, but I don't know if that's COTS for a reasonable price.
You can close the loop yourself by adding a small uC in the loop but where is the fun in that?
And what does this mean:
I should add that I occasionally want to have good torque at 2% of the motors rated speed,
DC motors are exceptionally good for high starting torque and overload peaks as long as the motor does not overheat (That will take time).
Brushed DC motors are often seen as a cheaper alternative for induction motors, but I don't understand why. Adding all that copper in the rotor, and the commutator and brushes should all add to the cost. I guess the main difference is that COTS induction motors are designed for industrial applications and last 50+ years while treadmill motors are designed to burn up after a few years so you buy a new treadmill.
I also had a short peek at Aliexpress for a "2kW Servo motor". These are PMSM motors, and 2kW costs well below EUR 500, and that includes controller and cables. These motors are designed for accurate RPM and position control. Just add some ball spindles, add LinuxCNC with a suitable interface and a bit of steel and you've got a decent CNC machine. Although for axes control, a 500W motor is probably plenty.
Horses are obsolete and PH has something to do with liquids.