That doesn't help, because my all-powerful admin session is as secure as the least secure page I access (or can be made to access) while on a compromised network.
Doh. Of course. It's all on the same domain. Do you think, that if designing a new application, it would make sense to make a separate admin sub-domain (assuming no wildcard cookies)?
Does the solution entail purchasing legit ssl certs for your static content domains?