Can you use a the vout of a regulator as the cathode and your full voltage as anode?
Not a good idea to do that with linear regulators - they are not push-pull outputs and if you attached a motor between the regulated output and the positive feed to the regulator, the regulator won't regulate any more.

What you are trying to build is a half bridge and if you want some kind of "neutral" mid rail for the motor return wire then use exactly the same circuit you have shown but biased to produce half the battery voltage.

But, then you have a H bridge in all but name so, why not just use a H bridge and avoid wasting heat in the "neutral" connection (or linear regulator should you find one that has a push-pull output).