There is another issue I need to address before finally getting to questions of how to actually infer a grid from a performance.
Imagine that we have a ritardando across two measures, m and m+1 such that Tm = 100, Tm+1 = 102, Tm+2 = 104. In other words τm = 2 and τm+1 = 4.
The tempo doesn't suddenly halve between measure m and measure m+1. We need to work out a decent model that adjusts each beat-group, beat and sub-beat τ appropriately for a continuous change in tempo.