Use stream profile for APM logon page

Have you tried to find this value in the customization section? I don't know of any string values in the logon page that aren't customizable. In any case, the HTTP_RESPONSE event in the server side context and is triggered when a response is received from the server. The ACCESS_ACL_ALLOWED event is in the client side context and is triggered on an HTTP request, but only after the policy is complete. In order to programmatically replace anything in an APM dialog, you'd necessarily need to layer an LTM VIP and iRule in front of the APM VIP. The iRule might look something like this:

when HTTP_REQUEST {
     remove ingress Accept-Encoding header so that server does not compress the response
    HTTP::header remove Accept-Encoding

     disable STREAM for the request
    STREAM::disable

     send the traffic to the internal APM VIP
    virtual internal_apm_vs
}
when HTTP_RESPONSE {
    if { [HTTP::header Content-Type] contains "text" } {
        STREAM::expression {@find@replace@}
        STREAM::enable
    }
}