Achilles and the tortoise, all over again.
A nice puzzle. But quickly disproved in practice.
It, of course, does not take millions of litres of water to wash a film as well as six changes of water do.
I made an honest mistake:
The FIRST filling of the tank works exactly like the first tank filling of the fill-and-discard method.
Therefore gallons should be reduced by a factor of 1/20th. But that wasn't considered a serious error in the days we used slide rules for calculations!

) Its the principle at work here, that's important.
After that slow dissipation is the name of the game, where the film and the TANK CONTENTS soil all of the water (and film) in the tank continously.
But as you say "quickly disproved in practice" since as already stated by Ilford, 3 changes is *enough*.
When we talk about just a 1/1000th reduction (Ilford method) of concentratiuon THIS IS MEASURABLE.
Because around there is the limit where there is "enough" and "not enough".
Beyond that is more or less pointless, a concentration so small its easily soiled by part of a drop of fixer under a fingernail.
But I stand by as a fact it is not possible to reach such small concentrations with simple watering of a closed tank, for any practical amount of time-, as by 6 changes of water.
You have this all wrong, water (and fixer)---- is NOT "flushed out of the tank", instead the concentration inside the tank is slowly getting lower and lower, described as a curve, it flattens out but *never* reaches zero.
In all qualitative chemical analysis 3 changes of water was standard operating procedure, and the little vials was placed in a gravitational tumbler/spinner, to separate fluid and non-fluid.
3 changes was enough. Trying to do the same with watering out & filtration would take forever. S.O.P.
Thrust old chemists, they used to do this every day.