Snapnames does not have an exclusive contract with the Verisign registry...
What Snapnames did was get exclusive contracts with a number of registrars before the dropped domain market had been identified as interesting by most of them. There was an interview posted with the president of SnapNames where he admited that they were very lucky to get these contracts early on. He did not offer up who these registrars were however - but he did say that these contracts expire soon, so there is good reason for SnapNames to be looking for alternatives like the WLS, where they have struck a contract deal with Verisign to provide the technology behind grabbing dropping domains. Which by the way, makes no sense to me since Verisign will be the dropper not the droppee.
The only way to compete is to get equal access to the registry - which you would only be able to do by striking a similar contract with an existing set of registrars, or by becoming ICANN accredited yourself.
Since the dropped domain market is clearly interesting now, no registrar is going to strike the kind of deals with anyone that SnapNames managed to do. It was a stoke of genius and luck - the two in combination that generally make one rich.
If you want to compete today, you need to become ICANN accredited and then write your own scripts to grab dropping domain names. This will let you grab dropping domains with the best of them today, and then to become a WLS "reseller" when and if Verisign takes control of the dropped name business for CNO names.
-t