My question was closed as not constructive, despite having some pretty decent answers. After some thought I can more or less see what was wrong with it, and I'd like to make it into something useful. Is it okay if I edit it completely, slightly altering it's meaning, if the answers given will still be relevant to the topic?
This is really three questions:
Is it acceptable to edit a question that got closed before any answers were accumulated?
To be blunt, if it has no answers the question was probably closed because it was crap. The comments may even be asking you to edit it so it's a good question and we can answer it. Fix it and let us know so we can reopen it if it's been reformed into a good, answerable question.
Is it acceptable to edit a question with a bunch of answers on it in such a way that slightly alters its meaning?
Like @MadHatter said we'd really prefer if you asked a good question the first time, but sometimes new information comes up (or someone asks a question in a comment that changes the way you look at the problem), so edits happen.
Editing questions means that people have to come back and fix their answers to take into account the new information. If your edits are going to require a lot of effort from the people who answered your question it may be better to just leave the original closed and ask a new one with adequate detail.
Is it acceptable to edit a question with a bunch of answers on it, in such a way that changes its meaning substantially?
If there are several answers and editing your question completely invalidates the answers, it's probably best to ask a new question.
If there's one or two answers go ahead and edit but leave comments on the answers so the authors know the question got edited and can revise or delete their answers as appropriate.
Interesting question. I was fairly heavily involved in your original question, both in answering it (to try to demonstrate that the entire question was founded on incorrect data) and I then voted to close it (since it increasingly seemed to be unanswerable once the error was removed). I'm not sure how you could "heavily edit" that question without making the answers irrelevant, and my guess is that it's unlikely the old question will get re-opened, so no new information will be posted as a result of your edit. My take is, if you think you have a better question to put to us, why not start a new question (though please do read the FAQ first!)?
But the content on this site is licensed under cc-wiki with attribution, which is posted clearly at the bottom of every page. So if you decide to ignore me and go back and completely overhaul the original question, then whilst I think that's not as helpful as posting a good new question, I don't think I can say it's wrong.