The OP is flying a light aircraft AFAICR.
Clearly the case from his cited example.
He is just trying to emulate the (somewhat imprecise) performance figures derived by the manufacturer test flying program,
Probably not quite the case. The usual design approaches adopted produce reasonably accurate and, certainly, fit for purpose, data for light aircraft. The more rigorous techniques applied by the heavy iron OEMs result in quite accurate performance information. Again, I would emphasise that there is a major difference between simulating AFM/POH data, for which one may attract a liability, and setting up routine monitoring protocols. For instance, in respect of the latter, every airline and the majority of other commercial operators will keep very tight records of inflight performance and maintain/update flight planning data to be used by pilots on the basis of individual tail history. However, takeoff and landing data in the AFM/POH is the basis for the pilot's compliance with legislated requirements. For example, in Australia, CAR (1988) 138 (1) imposes a specific responsibility on the pilot to comply with requirements published in the AFM/POH - I would be surprised to see a substantially different requirement in other jurisdictions.
If he follows my suggestion he will be able to derive a formula that will be well within the accuracy
This I would dispute in some, but not all, examples of AFM charts. It all depends on how the charts are developed. More importantly, the simulation has to produce accurate and defensible values for interpolation between printed data. So long as the simulated data can be defended conclusively in court, all is fine.
The great advantage of my suggestions is that it self-adjusts as you get more data.
Fine for route performance monitoring but not, I suggest, for the takeoff and landing concerns of the OP.
given the simplicity of that performance graph (largely linear with temp and wind, maybe second order with mass)
I presume you are referring to the cited example. Certainly a simple presentation but not much in it will be linear, I fear. Generally, in my experience, one is at risk going beyond a third order equation ... nor is that necessary. If it appears to be so, one needs to segment the line data.
remember my warning about extrapolation outside of limits!
This comment causes me some concern as it infers the use of needlessly high order equation simulations. One needs to keep in mind that extrapolation of certification data is a no-no and would be difficult to defend in court in the extreme.
I guess we just need to agree to disagree on a couple of points ?