Control Engineering: Model parameter estimation for a motor which will be under various loads

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.

Your magnet approach is the only one that is likely to work, but there are a number of gotchas. Be aware that stabilizing an attractive magnetic setup (rather than a repulsive one) is not for the faint of heart, and especially not for beginners. The problem is that the attractive force can get very high very quickly if the two magnets get close together, so the magnets tend to "snap" together faster than your system can respond.

First, there is no need to make the magnet currents independent. I'd advise making the two linearly dependent. If the lower coil current varies from 0 to 1 amp, make the top coil vary from 1 to 0 amp, with the sum constant. This is hardly optimal in terms of performance, since the two repulsive forces will not be linearly related with respect to displacement from the center position, but it will be far easier to control and stabilize. Think ahead - upgrading to independent loops will be a no-brainer for further credit.

Second, your encoder scheme, while OK in principle, is unlikely to work well. The problem is that, unless you have access to a really high-resolution encoder your angle measurements will be too coarse to give the sort of accurate position information you need. Not only that, but measuring angular velocity (the D in PID) will be very coarse in granularity, and for low rates will have a very slow update rate. Get hold of your encoder specs and pendulum arm length, and calculate just what your vertical quantization is. You cannot do better than this.

Third, you'll be able to do a simple open-loop calibration of your system simply by putting differing currents into your coils and seeing where the moveable magnet gets to, although you'll have to be careful about damping out residual motion. This is probably a better bet than trying to calculate position from first principles. See https://en.wikipedia.org/wiki/Force_between_magnets for a discussion of inter-magnet forces. Be aware that these results are very sensitive to small changes in geometry, including the size of your magnet cores.