Interesting case study, plasgears. The 172 and 182 are different animals, of course, but share many of the same traits.
There are lots of different 172's, but looking at the 1980 172N and the 1981 172P is instructive: The fuel arm is actually a little aft of the rear CG limit. This means that the CG actually moves forward as fuel is burned, so if you're in the envelope at takeoff, you're still in it on landing (unless you were so far forward loaded initially that fuel burn puts you out of forward, but such a loading is highly unlikely).
As they did with the change from 182Q to 182R, Cessna also increased the MGTOW from the 172N to 172P in 1981. The 182 increase was about 5% and came along with the CG limitation change mentioned above. The 172 increase was 100 pounds (about 4%), but there was NO CHANGE to the CG limits. (And unlike the 182, the weight increase was a Design Weight change, applying to both landing AND takeoff). What they DID do, however, was restrict the flap travel to 30 degrees from the previous 40. This was no doubt to maintain nose-down pitch authority, especially given a go-around at the new weight.
In your case, I assume flaps were deflected on final, and like all Cessna high-wing singles, associated with a pitch up to be overcome with down elevator. Nevertheless, I don't think what happened in your case was CG related, but I could be wrong.
As far as "running out of down elevator" in general, an interesting FAA Airworthiness Directive (AD 77-14-09) ominously entitled "Aircraft Controlability" was issued against the 182P and Q airplanes in 1977. Apparently, during flight testing for an autopilot STC, FAA found that there was insufficient nose-down elevator control during flaps-down, power-on flight. The AD required the aft CG limit to be placarded and moved forward 2.5 inches until the horizontal tail spar, if found uneven, could be bashed back into shape with a block and mallet! Turns out that defective tooling was turning out almost imperceptible changes to the tail spar, causing flow separation across the elevator.
Although the 172 and 182 share the same wing (flap limits in the heavier 172's notwithstanding), they do not share the same horizontal tail and the AD mentioned did not apply to 172's. But in your case, maybe something similar was happening? In any event, that's probably more than you wanted to know. Thanks for your post. Hope someone can answer that first CG question. CHEERS, Tom