I didn't think that we were mentioning any particular performance category, and to be frank I was just playing with equations to relieve the monotony of, well playing with equations at the moment.
In any case, if your proverbial flying-bus has a fixed value of Vr (which is fair, it is usually a function of VMCG for multi-engined aeroplanes) which is irrespective of flap setting and thus CL.max the only affect that has on my argument above is that the threshold condition of the first integral, Vr becomes fixed (so T - D becomes the only player), which is true for multi-engined aircraft only. For the second integral, if you are arguing that the delta-n value remains fixed because the flightpath isn't influenced by CL.max, then again the only real variable becomes T - D again.
Perf-A requirements include that V2 >=1.2Vs for singles and twins or >=1.15Vs for 3+ engines, (and it's always essential to reach V2 by screen height) so stall speed does remain a player for all take-off calcs unless a company has elected to use fixed values of Vr and V2 for all weights and flap settings, based upon minimum flap and MTOW - which seems unlikely. (Incidentally, Vr is also a function of Vs for singles, it's only for multi-engined aeroplanes that it's a function of VMCG alone.)
G