Thanks to a great suggestion from Rafal in Poland, I have a first working version in which a participant can watch video in way taking into account both their eye misalignment and also the binocular suppression ratio needed to get both eyes working. When they click “ok”, the video screen on the strabismic eye starts to straighten up, very slowly and gradually.
This is nothing more than a very basic proof of concept (audio isn’t working, there’s no way to select a stream etc.)… but it could be worked on to produce an interesting way for the brain to practice maintaining fusion (while it is engrossed in a film) with the added reward, that the more the strabismic scene straightens up, the more of the scene that eye can see (i.e. the less is hidden “off screen”).
Another possible approach would be to constantly be straightening the eyes, but for the participant to always be able to move the straightening back by moving their head. We’d set the ration very low, so a lot of head movement results in very little resetting of the video. This provides a genuine behavioural advantage to learning how to maintain fusion by moving the eyes, because that is a lot less awkward than having to constantly move the head and reposition in your seat!