All discussions of this matter are very old and are no longer really
relevant. Of course all simulation methods have a certain limit in
accuracy. As I told before, please visit www.cara.de and bring up the
menu item "Products/CARA/Walkthrough" and then select chapter II
(Calculations) and subchapter 6 (Comparison: CARA and Measurements).
From this one may judge the accuracy of cara simulations.

Comment regarding rectangular rooms: - any room with a rectangular
outline in the floor plan is no longer a rectangular room when several
pieces of furniture are introduced.

Proposal of a test case:
If you visit www.cara.de you will find our online service "CARA-Quick"
which uses a modal method like you propose (series of eigenvalue
functions). You may be sure that we checked very carefully the
methods used in CARA and in CARA-Quick by comparing their results.