That changes nothing. Still copyright infringement. See above.
This might work: Stop broadcasting the video. You make an audio only CD where you and friends play the parts in the movies. The customer is instructed on when to start the audio CD so that it syncs with the movie. You can also distribute a book that tells the person when to start and stop the movie/audio and then do your thing with your company.
So all you are selling is an audio CD, which you performed, and a companion workbook.
This MAY work because what you are doing is making a "cover song" of the movie audio. You will need a mechanical license, if it is even available. http://en.wikipedia.org/wiki/Mechanical_license
I have never heard of this for movies, but it might work. A mechanical license will be cheaper and easier than negotiating with a movie studio.
This is how it works in the music world: http://www.harryfox.com/public/FAQ.jsp
No idea if you can do this in the movie world, but you should check it out.
That is slightly different than OP because OP wants to broadcast the movie, or at least the exact words. The exact words are what he needs to license, even if he does perform them himself.
If OP can figure out a way to teach people language by making his own rifftrax mp3 then he is in business. Good call prodigal_erik.
The reason why is at the very heart of copyright law. You need to learn this area.
Owning copyright to a work gives the owner EXCLUSIVE rights to distribution of that work.
Therefore, just because you sold a legal copy to a user via Amazon you do not have the right to broadcast the work on your website. Only the copyright owner can do that, because he has exclusive distribution rights. Your broadcast isn't authorized even though you selling DVDs is authorized.
Be careful with this stuff. In my opinion you are playing with fire here. The RIAA has no problems with burying people who distribute songs illegally. MPAA has done less of this, but you don't want to be the example.