iRule redirects causing pool member issues

iCall is for 11.4. I'm only on 11.2. Is there any other way around this besides having to upgrade?

If you look at step 3 in the link, that's the basis of using a raw user_alert.conf config. Just execute your TMSH call in that exec command= section.

Do you think if we remove the pools in the iRule and replace them with a URL, will this issue be mitigated?

Do you mean URI's (different paths on the same web server), or URLs (as in a 30x redirect)?