You are probably going to have to reduce the screen resolution dramatically to get something down to 7.5 MB. H.264 can only do so much. You might need to reduce the video down to 640x480 to get even close to 7.5 MB using H.264. Full screen resolution is just too much for H.264 to get down to the size you want.
Non-destructive editing is an important feature of iMovie.
iMovie preserves the entire copy of every clip you place into your movie in case you change your mind at a later stage.
So, if you have cut out one minute from a 45 minute clip, iMovie will have stored two complete copies of that clip. This is why is helps to set import as 3-5 minute clips rather than one huge chunk. As DV runs at 13GB per hour your project files can get very big.
One workaround is to complete the editing of a section of the movie, then export that to Quicktime: highlight the clip/s, choose Share-Quicktime, turn on Share selected clips only, and choose Full Quality from the pop-ip menu.
Once you have saved the stand-alone clip to your hard drive, you can re-import it into your project using the File/Import command, and delete the original long clip/s from the project.
there are a few other 'knobs' to play with ... :
usually, there's no need for 30fps on a screengrab - who cares when the mouse cursor 'stutters'?
for a public viewing, 15fps would reduce file size by half.
next, for screengrabs, I wouldn't suggest h254 but Animation ...
last, and most important: bitrate. in the many option&sub-options of the Export with Quicktime dialog, you're allowed to set manually the bit-rate. for plain graphical content as a sreen-grab you can experiment with ultra-low settings, <1.000kB/s or even <500kB/s ... even for a 1920x1280 video (iM had changed the res of your grab into that res).
if the grab had a smaller res, you can re-size that on export in the same dialog too.
lowering frame-rate, bit-rate and probably resolution will help you to accomplish the goal.
for the last grain of quality on low bit-rate, I would also suggest the free x264-encoder which imho performs on low rates better than the original h264.-
Thank you everyone for the replies. I have done some more experiments but remain perplexed. I've used the "Export Using QuickTime..." option and created videos that have bitrates as low as 256Kbps, framerates as low as 15fps, and other such knobs. I have gotten the file down to 10MB, but the quality was terrible.
To repond to Brad's comment, remember that the original file was 7.5MB. And that file is 1280x1024, H.264, 15fps. This is what is so perplexing. I have matched the resolution, the codec, the framerate, and the bitrate. The file either appears 10x the size or at a much worse quality. And all I have done in the editing process is shorten the video by 25%.
The problem could be caused by the re-encoding of H.264. The encoder is expanding the noise and artifacts in the video caused by the first H.264 encode. You may record your original screen capture in a higher quality codec, such as Animation, AIC, ProRes, etc. It's the best thing I can think of. Other than that, I'm stumped too.