Back to the subject in hand...
...it may have reached max elevator to maintain the attitude for the speed at that height
This can be a problem with older autopilot types, even the NG aircraft have a rather basic autopilot, carried essentially over from the earlier models, with minor improvements...at least according to a good friend of mine who was an instructor on the NG series.
In fact, I asked him specifically about this.
Can you or 'your good friend' the NG instructor explain this one to me? Are you and 'your good friend' suggesting that the elevator would be maintaining max deflection throughout the scenario described by the original poster?
According to the B737 instructor, the NG autopilot is nothing but a rehashed older Boeing design, originally installed on the B737-200.
Further, the autothrottle system has poor speed control, in some situations.
And, worst of all, during CatIII ops (at least with the NG aircraft that his airline has) there is no roll-out guidance provided, IE: when the aircraft touches down, autopilot(s) disconnect.
Further, and I have been told this last observation by at least two other pilots who have flown the NG type (at two different airlines) that (and I quote)...'the airplane really doesn't touch down all that smoothly, rather it sort of 'flops on', without much finess'.
And, to answer you question specifically, yes, it has been observed by some pilots in the NG aircraft that the elevator has been out of trim in certain situations, because the stab did not trim properly, in the first place.
Shades of the 'ole B707 in this regard, it appears, which had a very similar problem.
We didn't have a problem trying to understand a totally analogue aeroplane There was no advanced technology involved, poor design, poor build quality contributed heavily to poor reliability, we just didn't see the logic of trying to operate a fleet of aircraft that were so labour intensive when the rest of the fleet we maintained.
I find this quite strange, especially the 'reliability and poor build quality' part.
I was told personally that DAL, the largest operator of the type, experienced the best fleet-wide reliability, with their L1011's (versus other aircraft), and they had quite a few other types, at the time.
Lets see, other TriStar operators were EAL, ANA, TWA, CX, GF, SV, RJ, and even small UL.
These other airlines didn't seem to have many problems with their aircraft, so it would appear that 'your' airline either a) could not maintain the airplane properly, or b) a corporate decision was made above your pay grade, to dispose of the type.
Yes, the L1011 is a complicated airplane, alright, however in my twenty eight years of flying it in command, I can offhand remember only a few technical delays...the last three years, only one, a deflated tire.