Is t a good idea? Generally, no. There's a school of thought from some in fandom that if authors repub their fanfic as original, some of these people will boycott and/or leave bad reviews. Sour grapes at being "made" to pay for work that was previously free. Not cool, not fair, but it exists.
If you're traditionally publishing, the publisher will want no evidence of the story being online, in any form or formal. So even if you pulled down...say HIPS, if it was cached anywhere, at any time, that could invalidate a contract.
If you're self publishing, it is a matter of what your audience wants. You have a huge readership,and I'm sure lots of folks will buy anything you write--completely new or redone (*waves credit card around hopefully*), but the thing is, will everyone? Will folks who read HIPS want to read an original fic version of it. And will the fact that we (your audience) "know" these characters as John and Rodney, Gibbs and Tony, change how we feel about the fic.
It is a lot to think about...
It can be done well and you definitely have the chops and talent to do it! But should it be...
That is a stickier issue.
Speaking strictly from a personal POV, I'd rather the fanfic stays fanfic and is used as an inspiration for new work rather than a template. That way the reader gets it all, so to speak.
And speaking as a writer, I find it much much harder to revise anything and make it conform to a new concept than I do writing an original fic.
I agree with what tejas said.