Uuniversal persistence for HTTPS

First are you off loading SSL to the F5s? If not you will not be able to read any of the HTTP Requests/Responses.

If needed to be HTTPS to the Server apply a Client and Server SSL Profile to re-encrypt the traffic.

Once done recommend you simply apply a standard Cookie Persistence profile.

You issue of all traffic sticking to a single pool member after a pool member has gone down and is now back up is a common one. Getting timing of your persistence to match the application will minimise this but most like need to wait for connection to bleed from the one pool member which should happen over time.

If this is a huge issue might want to look at additional back end servers or a manual step to clean down the connections, but this would disrupt many of the user sessions.

Hope this helps.