The line between parody and satire is very thin, and between fair use parody and non-fair use parody it is even thinner. You really need to get your song cleared by an IP lawyer who can review both what you've written and the original. There are a lot of cases that go back and forth on this issue, but the general rule is that, for fair use, you have to be commenting on the original work from which you are working - here, the song - and not another person, thing, or idea. If your parody isn't directed at the song, it has a much, much thinner chance of getting fair use protection. Satire - general commentary on culture - is never enough for fair use, and parody must be criticizing or commenting on the original work to enjoy fair use protection - keep these two rules in mind and have someone check your work.
Also, as the other attorney pointed out, fair use is a defense - it only comes up when you've already been sued. Which means that you're going to end up spending money for a lawyer, anyway, once the artist gets wind of what you're doing to his or her song. It's much better to get out ahead of that by hiring an attorney now who can either tell you your plan is unworkable or help you find a way to make it work.
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As another frequent poster here can tell you, Weird Al Yankovitch always gets clearance for his parody songs and he has much better argument for free speech, commentary, and fair use than you do with your commercial parody. A judge or jury is more likely to think you are merely a ripoff artist rather than a satirist. Yes, if you want to stay out of court, you need permission, even if technically, you might be able to convince a judge that the primary purpose of your infringement was parody rather than making money. I, for one, think you need to stop in your tracks and drop this idea.
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Well you don't need permission to produce a parody, but realize that parody is a _defense_ once you've been sued for copyright infringement, and that permission from that possible claimant avoids that concern.
And yes, Weird Al Yankovic sort of ruined it for all song parodists by never picking fights with those whose songs he parodies by giving those songwrighter _all_ of the publishing copyright on the parodies he performs. So even though he writes his own lyrics to their famous songs, he doesn't claim any ownership interest in those songs. And as my colleague notes, his lyrics do comment directly on the song itself and/or on its songwriter, which would greatly increase his odds of winning a parody argument, if he ever engaged in one.
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