First, psychosomatic illnesses including conversion disorder, are almost certainly always a false diagnosis. There is no objective evidence such diagnoses are valid diagnostic entities. They are most probably fictitious.
On virtual reality, there is a reason many of us are gamers. If you have looking at this kind of experiment, then gaming is where it is at. There are not walking simulators, but there are many games in which you can walk while in virtual reality. Gaming gets me out of my limited living space, and creates an illusion of another life. Its like a holiday ... its not my life but its a welcome escape.
However I seriously doubt it will be of benefit for PEM. I do not yet have a virtual reality headset, its on my todo list. However I know someone who has done this. In general, virtual reality creates massive rapid vertigo or crash. The brain is overwhelmed. However new advances in virtual reality have at least partly fixed this. There is at least one ME patient currently playing Skyrim VR with only minor issues. It has not retrained the brain though. According to what I have heard, its peripheral vision that is the main problematic issue, and Skyrim VR deals with this by limiting peripheral vision during movement.
If there are other ME patients playing VR games, please let us know your experience.
PEM is, according to the best current science, probably not primarily an issue with the brain though the brain might be affected. Its an issue with biochemistry. Now the brain might be orchestrating some of this, but its exceedingly unlikely it has anything to do with visual processing.