OK. Sounds like it's HTTP at least... And I'm assuming here you have access to the stream (As you used to do cookies), so there's no problems there. The BigIP can persist on other information in the headers... All you need to do is to find out which headers the application itself is using to track the individual users and persist on that...
You'll either have to tcpdump the traffic and work on decoding it, or speak to the developers who wrote the frontend/backend software and ask them.
Then create an iRule that will decode this information and select a persistence entry. Match that up with a Universal persistence profile and you should be away.
H