Questions first, I suppose:
The more I think about it, the more unreasonable actually joining the SS seems. The kind of deep-cover background that gets agents into an organization like that takes years to establish, and I don't think we have it; and furthermore, I'm not sure any of the characters we have at the moment are the kind of Aryan ubermensch the SS recruits.
So let's take a step back and think about this. As I understand it, the task is not strictly to infiltrate the SS, but to get close enough to Himmler to find out whether the inner circle knows about or is attempting to use any Secrets Man Was Not Meant to Know (SMWNMTK).
The only way I can think of to get close enough to get a convincing answer to that question is to approach someone high enough up with secrets to sell. And that means, some secret interesting enough to get us in to talk to someone serious. It's a kind of lunatic dangerous game, but I can't think of anything better.