I would certainly like to see the references posted.
The eye movements used in EMDR are theorized to catalyze the information processing system. In your experiments, as in REM sleep, the question is how are the eye movements related to the processing and the observed physiological changes. Since the eye movements in your experiments, as in REM sleep, are spontaneous rather than deliberate are the eye movements the product or the precursor of processing?
In EMDR sessions the eye movements, or other forms of rhythmical stimulation appear to move information at a rapid rate. As another person has posted on this website--it appears to be free association in "hyperdrive." Both REM state and EMDR rapidly cause emotional processing and learning to take place. In fact, Jonathan Winson is the sleep theorist most closely akin to EMDR's information processing theories. There are a variety of similarities between EMDR and REM-sleep effects and it may be that the deliberate activation of similar eye movement activities link into the same processing mechanisms. However, clinical observation clearly shows that processing of information is possible without imagery. It is also observed that other forms of activities stimulate the same processing effects.
I hope others with experience in your area of expertise will be able to comment. In the meanwhile, I would like to hear some of your theories in more detail.