I have to admit, I'm confused by your spreadsheet, as the data it contains aren't based on either the original Perronet model or what you have labeled the "simplified" version (which actually has more adjustable parameters). How did you come up with the numbers that are shown?
As for Excel, it does contain a Solver function as one of the Add-ins. It isn't quite as full-featured as you might find in a full-blown stats or curve-fitting program, but it can get the job done. In fact, I used it to cross-check the solutions provided by other programs (e.g., GraphPad Prism) and the WKO4 solver when developing and validated the model. This proved to be really important, as there are some hidden "landmines" that could have easily gotten overlooked otherwise, at least until it was too late.
ETA1: Here is the Peronnet-Thibault model looks like when you fit it to all of the data. Parameter estimates are as follows (values in parantheses are 95% CI):
A: 13703 (13485-13922)
MAP: 226.5 (221.2-231.9)
E: -11.03 (-13.98--8.075)
ETA2: And here is what your "simplified" model looks like:
FRC: 20246 (18206-22301)
tau1: 28.6 (25.3-32.0)
FTP: 210.0 (205.6-214.4)
tau2: 101.2 (78.3-126.3)
ETA3: Finally, for completeness here is my model:
Pmax: 712.8 (685.9-739.7
FRC: 9065 (8602-9602)
FTP 241.2 (237.7-244.6)
TTE: 1976 (n/a)
Stamina: 84 (81-85)