Best method to rewrite Request and Response URI, preserve URI data, and with no client redirect

Try adding the default stream profile and using and iRule like this:

when HTTP_REQUEST {
    HTTP::header insert "SetContextURI" "http://[HTTP::host][HTTP::path]"
    HTTP::path [string map {/123 /321/PRServlet} [HTTP::path]]

     Disable the stream filter for all requests
    STREAM::disable

     LTM does not uncompress response content, so if the server has compression enabled
     and it cannot be disabled on the server, we can prevent the server from
     sending a compressed response by removing the compression offerings from the client
    HTTP::header remove "Accept-Encoding"
}
when HTTP_RESPONSE {
    STREAM::expression {@/321/PRServlet@/123@}

     Enable the stream filter for this response only
    STREAM::enable

    re-write Location header
    HTTP::header replace Location [string map {/321/PRServlet /123} [HTTP::header Location]]
}