Is there any way to get the Shotcut output file size down to anything close to the Avidemux size?

When exporting, on the Codec tab:

  • Set Rate Control = “Average Bitrate”
  • Set Bitrate = “1M”

The output file should be about 2MB. Click “dual pass” if you want the extra quality boost. If you want an even smaller file, choose a lower bitrate.