The help center article titled "What if I disagree with the closure of a question? How can I reopen it?" now goes into more detail than the old FAQ entry did. It does not explicitly instruct users to flag their revised posts for moderator attention, as that's not necessary a lot of times (especially now that any substantial edit places a closed question in a review queue to be considered for reopening), but there's more information about how and why a question might be closed, as well as some more specific guidance on what to do about it.
As I mentioned in an answer to a different question about closingan answer to a different question about closing, this is a problem that we're aware of and working on. We're exploring our options and trying to come up with a solution that will be clear, easy, and useful; the problem is not quite as simple as your question makes it seem. Sure, we could just add more text to the already long FAQ section...but honestly, very, very few people ever read the faq, even if they have a specific problem that could be solved by reading it.
This is a twofold problem:
- We need to find a better way to encourage users who vote to close to leave a helpful comment explaining exactly why the question is a bad fit for SE (which part of the scope does it violate, how is it too localized, etc.), and
- We need to motivate users whose questions are closed to come back and improve them when possible.
The latter is pretty difficult issue; if a question is closed, it's often because the asker isn't familiar with the scope of the site, or they mistake SE for a general forum (ask questions that don't fit our format). For those users, do we first try to teach them how to get their question reopened and then hope that they'll read another page about what questions are on- and off-topic, or do we try to get them to understand the scope of the site and the SE philosophy before telling them how to possibly get their question reopened? They're both really important goals, but most people will not care enough to get through two separate tutorials/walk-throughs.
Your proposed FAQ changes aren't bad, but you fall into your own complaint of it being "overly detailed". Jeff's points about the wall of text and encouraging whining remain valid. Additionally, the part about "do not post your question again" isn't really necessary; if someone posts a question that is identical to one that they previously posted and was closed, it should come as no surprise that the question is closed a second time. If the question is posted in a new, better form, though, that's totally fine - closed questions are supposed to be deleted eventually anyway, so this shouldn't cause too much clutter.
I appreciate you bringing this issue to our attention again; it is definitely a part of the user experience that needs improvement. Unfortunately, I cannot promise you an immediate, concrete solution, but I can tell you that it's being discussed and we hope to fix it soon.