It would appear this is all part of Microsoft's new Identity framework which basically replaces Membership.
Following a mixture of this tutorial for adding Identity from scratch and this tutorial about doing a migration from Membership to Identity I managed to get Startup firing properly.
HOWEVER - if you are reading this and are in a similar situation I would think carefully and evaluate the Identity framework against all of the alternatives available both from MS and other sources before jumping in. At the time of writing, I would would say that the Identity framework isn't currently ready to be used in a production application and others seem to agree. Looking at the road map I've no doubt it'll get traction once the features are padded out, however at the moment it requires too much work for it to be workable for me.
Looking at my requirements I will be sticking with my custom membership provider and will add my external logins on top using DotNetOpenAuth.