Video Playback - Need a way to make students watch the entire video without taking away their controls.

I Think you're overlooking at least one other option here...

if you want to ensure that people watch your entire video, make it so darned interesting that they don't want to miss a thing.

Adult learners tend to resent being forced to watch boring content. Any strategy based on "dictatorship learning" is counterproductive.

It is possible if you build your own player in flash if you are using swf output. I;m sure it could be done with javascript in an html situation also.

Think about it. How does taking away their ability to NAVIGATE prove the learner actually WATCHED the video?  They could still easily go do something else while the video is playing.  Does this somewhat draconian 'state' of which you speak also mandate that someone is present when the student is forced to watch this entire video to verify their compliance?

This whole approach is futile.  Get the person to tick a box either at the end of the slide or on the next slide requiring them to verify they DID watch the video in its entirety.  If they choose to lie, it's on their adult head.

It's the only way if you want them to be able to navigate to the portions of the video thay ahve seen, but not unseen portions.