Here's how I made a 20mb GIF that is impossible to upload to most free image hosting services. This is using 10.6.8 on an old MacBook Pro but nothing here is platform specific. At the end of the day, you're just treating a sequence of image files as text and round-tripping animation.
Export video as an image stream.
I used MPEGStreamclip and saved a big folder of JPEGs. File>Export to other format. Select 'Image Sequence' from the drop down menu.The problem with this software is that you need to pay extra to extract DVD video frames, otherwise it's free. At this point I also made a reference version of the folder (copy/paste in Finder).
Use a text editor to do folder-wide find/replace commands
My favorite text editor on OSX is the free Smultron clone Fraise, but that actually crashed when I tried to do a find/replace on ~400 files all roughly 500K in size. Thankfully there is another program out there called MassReplaceIt that does this quite well. For a person comfortable with a command line text editor this would also be pretty easy to do, but then the screenshots wouldn't look as pretty:
Turn it into a GIF, or some other video file.
I like this option because you don't have to deal with more image artifacts but you could go straight to any video format with the right tools. Did it with GIFfun.