one might be able to derive some sort of formula

Equation (9) in the paper referenced in post#27 gives the minimum drag speed Vmd. It corresponds to a lift coefficient equal to √(Cd0/K).

If Vmd1 and Vmd2 are the minimum drag speeds at different weights, then the speed at which the airplane has the same L/D at both weights is given by:

V = √(Vmd1*Vmd2)

P.S.

A pretty useless formula, isn't it? It took me a whole evening to work it out. Just for the fun of doing it. But the result is a beauty, for those open to it.