App to convert large amounts of video files

You will need the HandbrakeCLI application that will allow you to set up a batch processing command-line sequence that is applied when looping through the .avi.

See Handbrake Documentation : Table of Contents. CLI Options. Command Line Reference.

With the CLI, you can set up a batch process in your favorite shell, or AppleScript (because Handbrake has an AppleScript dictionary). Here is an example of Handbrake usage in AppleScript.

I just took an existing .avi and using the Handbrake defaults converted it to 720p .mp4 without issues.

Try HandBrake: https://handbrake.fr

There's also ff-Works.

https://www.ffworks.net/