What method of implementation would you prefer?

A. Transcripts are visible on the video at the bottom according to the time stamp (similar to closed captions).
B. Entire transcript is visible as a list in a scrollable div container under the video, and the appropriate line depending on the seek bar is selected / auto-scrolled.
- Collapse / expand box, collapsed by default?

We're just doing for the HTML5 player. Implement subtitles using a <track> element. Don't worry at all about how it is styled, we will leave this to mediaelement.js/accessibility-tools/browser/themers.

https://developer.mozilla.org/en-US/docs/Web/Guide/Audio_and_video_delivery/Adding_captions_and_subtitles_to_HTML5_video

Don't write any JavaScript.

I don't think we need to be concerned about the different between transcripts/captions/subtitles. Just implement something working, and that's a base themers can expand from. The primary aim is accessibility, not internationalisation.