A GA plane will definitely fly faster at a given power setting by moving the CG aft.
For safety's sake they are built with the CG far enough forward to require stab/elevator down force for level flight. By moving the CG aft, less down force is necessary, and with the resultant lessened induced drag more power is available to pull the airplane forward. Therefore, a higher speed at the same power.
Bill.
That was a concise and straightforward explanation, just as simple as "two plus two equals four".
And we really don't need to know about the fella Doolittle in order to understand that.
Thanx