I'm trying to download some videos from dropbox that the account owner has disabled downloads for. Are there any tools or methods to bypass this and download them anyway other than screen recording?

Have you tried using JDownloader? Copy paste the URL to it, and see if it can scan and find the video. Not sure if that would work, but there's a good chance.

If it doesn't work, try yt-dlp.

You can try using inspect element and see if the links to ths video files are available that way.

if its ok could you link that file here? i've never seen such example so can't tell but i doubt they have strong (or any) drm

this is iffy, but you can use the inspector and try to find which of the files is the video you want, then download those manually.
Less iffy, use obs-studio and record the videos like how we used to do music in cassettes (in real time).