Can I drive a stepper motor like a brushless motor?
Yes, you can run a stepper motor closed loop, and that's the way to get the maximum performance.  However, that's not what steppers are designed for.  They are optimized for open loop control.  You might be better off with a geared BLDC motor than a stepper motor for what you're trying to do.

One problem with closed loop control of a stepper motor is that stepper motors have many poles.  This means a complete magnetic cycle is only a small angle of rotation, often just a few degrees.  A shaft position encoder would need enough accuracy and resolution to reliably indicate the magnetic phase with that few degrees.  That won't be cheap.

If I really needed to do this for some reason (so far used geared motors for such applications), I'd try sensorless drive.  This looks at the voltages generated by undriven coils as the rotor spins.  The problem with this is that it requires the motor to move.  I think for a stepper the firmware would also need to keep track of where it thought the motor was, and intelligently fall back to traditional micro-step open loop control when going to slowly or loosing track or getting data back that doesn't make sense (which indicates lost track of position).

Again, go use a geared motor.