I've never seen MIMO used in this context before, but I can see how SISO might apply.
Most robotic systems I've seen have been aggregation's of single axis motor controllers (your multiple SISO) each of which only had a single encoder for sensing and a single motor for actuation. So each axis was SISO, but the robot as a whole was MIMO.
Some systems I have worked on had significant backlash between motor/rotary encoder and load/linear encoder, so implemented a dual feedback loops, with one motor control output, but two encoders. The rotary encoder on the motor was primarily used to track velocity accurately, while the linear encoder on the load was used to compensate for backlash in the (worm) gear and provide accurate position information and tracking.
I believe that for most control systems, these traditional control methods are the most you will ever need, however there are exceptions.
I have only seen one system which might have benefited from a truly MIMO control system and that was one with similar characteristics to your own, but also needed to control the force applied by the tool-point of the robot. We did implement this with a traditional multiple SISO approach, but it required exceptionally careful tuning, and I'm not convinced that trying to use some form of computed torque technique would have been any easier anyway.
I would suggest that you start off with a multiple SISO approach and if that fails to give you the performance or characteristics you require, research into more advanced methods. At the very least you will have learn a lot more about the kinematics and dynamics of your system by that point.