Regulating D.C. motor – Feedback

Your approach should work. It's also the simplest way to solve the problem.

You could always work out a position controller that steers directly the motors, but it would be less easy to understand how to tune it. And I understand you have both position and velocity readings, so why not using two loops?

As people's comments to your question highlight, obviously you'd now have a position controller rather than velocity. But it makes sense as it's for a robot.

You need to be careful to a few details:

1. If the two DC motors are working in parallel, you must find a way for the two not to interfere with each other (like forcing load sharing). However you must have faced this problem already in the speed loop.
2. The external loop (position control) is bound to be far slower than the speed loop. If it worked at the same pace, or faster, you'd have the position loop strongly pulling on the speed one without letting it the time to react, and you'd have strong interactions or even instabilities. I suggest that you speed up the internal one (speed) as much as you can, and then tune the external one.
3. The external loop shall here be your 'precise' one. The internal one should just be quick in reaction rather than precise. I'd suggest a P or PD controller for the internal one, and PI or PID for the external one.

Extra tip: as it's for a robot, I'd take into consideration a position reference feed-forward.

You did not mention what min and max speed is required. I suppose you don't want to make any compromise in any parameter ;-)

With stepper and microstepper driver you can achieve better than 0.15 degrees resolution. But what is precision ? Probably wrong because there is motor and microstepping non-linearity and torque is low, dynamic range is low and extra problems come at very low speed.

You can arrange it as dual loop control with load encoder at outer loop. It should improve precision. Let say 13bit load encoder and 32 or 64 microstepping with 400 step motor might satisfy 0.15 precision.

Gearbox helps with torque and resolution but you also need dual loop control and no backlash if you want change direction. There is extra problem if there is a spring in gearbox. If yes then there is a force at output you need high frequency control loop. It might be even impossible to control system when you must consider this force. So expensive gearbox or back to direct drive.

You can substitute stepper with brushless 3 phase motor and encoder with or without gearbox and one or two encoders. Dynamic range and price go up. Torque ??? For high speed you need high bandwidth encoder/decoder. And it's very difficult to debug such a setup in real time as you almost cannot use breakpoints.

Generally when using encoders they must satisfy your precision needs (and not resolution only).

EDIT (as commenting is forbidden): AS5045/8 encoder: I think you need consider mainly non-linearity INL parameters in range of degrees which affects accuracy (worser than 0.15 deg). Also propagation delay in range of 100 us limits speed, 1RPS = 1/4096 = 244us per position tick.