MathWolf, right, your solution does not turn Bayeselo into Elo, I was only implying that it will make it behave more similarly in the early phases of rating.
As to your last paragraph as to where you see how Bayeselo can be improved, you may be interested in this link:
http://remi.coulom.free.fr/WHR/
It is a paper describing a new rating system, designed by the same person as the Bayeselo system currently in use for Warlight. The paper is title titled "Whole-History Rating: A Bayesian Rating System for Players of Time-Varying Strength" (in my opinion this is just about the same as saying "A Bayesian Rating System for Humans, not Machines"). Unfortunately, I don't think there is currently a downloadable application for this newer rating system, but maybe I will email the author to ask. I'd be glad to take a stab at programming a small application to run the calculations with this algorithm, but my math skills are frankly not sharp nowadays. I'll have to read through the paper and see how explicitly the system is spelled out, to determine how feasible that would be.