Maverick, you must add the PAPI setup transition angle between each beam to your assumptions.
Even then, whatever relationship you determine between PAPI and ILS, in practice when descending and deviating from the required GS you have to consider both vertical and horizontal components of flight path, which in turn depend on range. Thus it is difficult to determine which component of flightpath relates to the change.
The advantage of PAPI over most other visual guidance systems is that it provides a sharp transition between colours. This because each beam uses a lens to focus the colour separation - like an old style picture slide projector, and therefore is very precise.