Thanks very informative but it does not seem that you are aware of the architects of Kelly, Ziemba, and Thorp use for equities the kelly criterion of
Kelly =
u(geometric Brownian motion drift) - r(risk free interest rate)/sigma^2
you use the drift, not the mean of log returns,
They have multiple variations of this formula, one for multiple shares in a single portfolio, and Ziemba utilizes a stochastic dynamic programming approach to dynamic rebalancing through intemperol investment periods, the above equation you discussed was only used by them for horse racing and blackjack, not the stock market, it is applicable to option trading NOT shares.