Persistence Exemption?

You can use an iRule where you disable the persistence (= persist none) for connections from the proxy address. Hope your application is stateless and can handle the connections right without persistence. Possibly you can use different kind of persistence for the proxy connections.

There are several threads where this is discussed. For example see https://devcentral.f5.com/questions/disable-persistence-for-fallback-hosts, first answer there.