Security limits of password-based encryption
An $O(\log l) $ cost for $l \le m$ seems a little simple given the many components (Argon, AES, hard &amp; soft optimisations and bounded RAM &amp; I/O).
Have you considered an empirical simulation?  You could lash something together in your favourite programming language, set all soft and hard parameters to reasonable levels and just see. So either an iterated approach, or a Monte Carlo simulation. It might at least suggest a real world relationship between all the parameters.
I don't know whether they'd talk to you about scale, but is it worth asking someone who actually does this? Apparently the Inmanis appliance has 'monstrous performance'.
P.S Whilst the application of your theory to a singular very large message seems sound on the face of it, the password wouldn't be recovered from such (knowing the presence of AoNT). Clearly you'd attack the shortest  message which might be &quot;Toodles&quot; covered by the same password. Don't know whether that has any bearing on what you're trying to demonstrate.