To clear up some things:
Looking at where business names (like snapnames.com at Register.com) are registered is not an effective way to determine business relationship among expiring names players. You can, however, watch where names Snap/NW/Exp Fish et al grab for clients end up registered at to determine who has what resources.
Namewinner is Dotster; I know that Dotster also partners (or at least partnered?) with Registration Technologies to grab names for NameWinner customers.
SnapNames is partnered with VeriSign, Namescout, Domainpeople, and several others I think.
I don't know who Expirefish is associated with, but in looking at their success rate, I don't think they actually have any SRS connections to seek names.
Each accredited registrar is allocated a certain amount of their connection to the registry to use (if they wish) for seeking deleting domain names. Small and large registrars have the same amount of bandwidth that they are allowed to use for this, so registrar size does not matter. If you are tying to grab names manually, however, the speed at which a particular rar actually submits your request will make a difference.
The goal of gaining of these registry connections would be to increase the ping rate a Snap/NW type service could apply to a single name. The faster the rate, the greater the chances that a name will be acquired by the seeker.
It would seem like the equation to determine ping rate would be something like this (and I'm sure this discounts all kinds of variables I don't know about):
SS = script speed: the software being used to send requests
BW= bandwidth: the amount of registry connections a seeker has
NN= number of names going after in that particular drop
SS x BW
---------- = Ping rate
Someone who knows more about the mechanics involved could probably help out with the relative importance of SS v BW, but I would guess that the above is pretty accurate.
I'm sure theres folks out there smarter than you and me making plans re how to game the system the get WLS slots. I don't know enough about the current WLS proposal to know if there are plans to prevent (or try to prevent, anyway) this sort of thing.