As said, I perceive there is a problem of using many independent compartments when there are strong pressure gradients between them, neglecting any gas transfer directly from one compartment to another.In the case of a single inert gaz, I'm not convinced by your argument. I've not make the computations be to be sure (I fear that's the kind of maths I'm no more used to do), but think of how Thévenin's theorem in electricity shows that any passive linear circuit is equivalent to one resistor, one inductance and one capacitor. Having a more detailed circuit could help to map compartments to physical organs, but I don't think it would give more meaningful dependency on the dive profile when you consider that the current one have already to take into account the variability of the sensitivity of any diver at different time, and between divers (for which GF is providing us a way to tune). My intuition is that you'd need more than cross-coupling factors, for instance some non-linearity in the DE, between compartments to get something new.
I'm less familiar with how multiple inert gaz is handled. My intuition is that even the little I've been exposed to would have dive-profile dependent effects in a more complex circuit (with several compartments having the same time constant but different cross-coupling).
But I have not enough knolwedge for proposing a proper lattice model, where gas transfer from one compartment to another is possible.
As we treat these gases as perfect gases, the fact there is only one gas, two, or more is substantially irrelevant, as in perfect gas theory each gas behaves and moves only based on its own partial pressure, and the partial pressures of the other gases in a mixture is irrelevant.