I just had a horrible, thought...
Consider something like:
tmgb = τmgb(b - 1)
We're not properly considering the length of earlier beats in a beat group in determining the offset of later beats. Consider G=1, B=3 (which I've suggested above would be 3/4 time).
tm11 = 0
tm12 = τm11
tm13 = τm11 + τm12
So obviously, if τm1* are constant then,
tm1b = τm1*(b - 1)
as before but if not constant we really need to take the sum.