I don't think retained cache is your problem. Quite sure that if you just close the browser, and re-open, without clearing cache and browser data, your site will load too. Personally I'm not a fan of F5-served HTTP 200 maintenance pages (prefer 302 to ext pages), but you can pull it off.
You will need to add
Connection Close
header to make sure client tears down the existing TCP connection when a static F5-served response page is received.
when HTTP_REQUEST {
if { [active_members [LB::server pool]] == 0 }{
HTTP::respond 200 content "[ifile get LNS_Sorry.JPG ]" noserver Cache-Control no-cache Connection Close
}
}