Try OneConnect if you have an HTTP profile attached. The other thing to note is that each backend connection will now carry requests from a mix of users. Almost all application servers these days are fine with this, but a very few may break (for example, if they only check authentication on the first request of the connection). The only way to know is to test.
Read the support article K7208: Overview of the OneConnect profile.
I can't think of a solution if you don't have an HTTP profile. Depending on your system, switching from fastL4 to Standard could add load, and I don't know much about RTMP to say if it's compatible. The TCP::close irule command can close the connection, but the problem is what event to trigger it with, since it's an L4 VS.
You can of course drop the connections manually through TMSH. (delete /sys connection). Maybe this could be automated with the tmsh scripting API, but I can't say if this is a good idea.
I'm interested to see if others here have more ideas.