The Favorskii rearrangement has been much studied so I doubt that I can add anything to what has already been done. I think the proposed mechanism is more of a "what else could it be" than a definitive proof. In my mind, it still leaves some aspects open to question. For example, the spirit of Baldwin's Rules is that the bond forming electrons should overlap with the leaving group. I find it difficult to understand how the pi-electrons of an enolate should enable a back-side attack of the C-Cl bond. I'm not saying it doesn't. I am saying I don't have a better mechanism either.
Regards to rates, we should examine all of the possible reactions that may occur, addition to carbonyl group, deprotonation of alpha-chloro hydrogen, deprotonation of opposed alpha-hydrogen, etc. These are all plausible steps. If the reaction path is faster for one of these steps, then we should conclude these steps are either reversible and did not lead to other products or they are slower.