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I'm not sure I understand the rest of your requirements, but I'll take a stab at addressing them.

"Redirect rewrite" will only rewrite redirects, not embedded links, and then only will change the redirect target in 1 of 3 ways:

1) rewrite the scheme from http to https for redirects matching the original hostname

2) rewrite the scheme from http to https for redirects to any hostname

or

3) insert the VS address in place of a real server address

You probably want to enable 1 since it sounds like you're decrypting @ LTM, but I don't think that addresses your "other private hosts" issue.

You can use the stream profile to replace the hostnames with different ones in embedded links as detailed in this article (Click here), but the hostnames would still have to be publicly resolvable names with publicly routable addresses defined on the LTM, and you'd have to define separate pools for each set of servers and then select them with an iRule:

when HTTP_REQUEST {
  switch -glob [string tolower [HTTP::host]] {
    *host1* {pool pool1}
    *host2* {pool pool2}
    *host3* {pool pool3}
    default {pool pooldefault}
  }
}

HTH

/deb