Would this officer calculate a higher value of Edef, a lower value of Edef, or the same value of Edef if he used the velocities of the cars measured in his reference frame?

The officer would calculate the similar value of Edef.

Explanation:

As Edef is the energy required to deform the body therefore the reference frame does not affect the calculation of energy. In this context the value of Edef will remain same irrespective of fact, whichever frame of reference is used.