Mark
Stick force (Pitch) simply put, describes the authority required to rotate the mass around its cg. Brian mentions "G" and pitch force lessening as cg moves aft. It 's true, if one wants to pitch up. It is increasingly more difficult to Pitch the nose down as cg travels aft. The reason is clear: with more weight (Inertia) near the Tail, the elevators must perform more work to resist gravity. Do I miss your point?
Addressing the original question? An unaccelerated a/c flies straight and level with all forces balanced (cwatters). Let's try to reduce drag. Assuming the cg is at a point that allows aft movement, and any change isn't other than benign, move the cg aft some small amount. To compensate for the resultant Pitch up (and increase in AoA) lets trim the tail (elevators) and bring the nose back down. We will note with satisfaction that the added drag of the trim (increased lift @ tail), has reduced the AoA of the Wings. This slight reduction in OVERALL drag is the payoff in lower fuel burn rate.
If we have gotten too enthusiastic with aft cg, eventually the elevators will be unable to keep the nose down, and that's the final outcome. The picture is clearer with a discussion of tailless a/c, and how challenging flying that critter is.