Can add my voice to the "BigIP should do this" school of thought. If it's
effectively converting HTTPS into HTTP requests for you, then I would expect
it should be able to rewrite redirects automatically for you too. Same way
that apache does it in mod_proxy.
However can I also point out that even if you catch redirects, you've still
potentially got broken HTML etc etc to "fix".
That would be cool if it did, but I haven't seen or read about a feature in it that does that. Even if it did, it might also incorrectly change redirected URLs, i.e. where the user is explicitly redirecting to a non-SSL absolute URL in the same domain, as opposed to my issue where something like mod_rewrite is generating the full URL from part of a URL, e.g.
RewriteRule test1.htm /test2.htm [R,L]