I’ve not heard Jim Bush mentioned by Francis or Mills, but John Smith has been mentioned by Francis. I think someone on here posted that both Francis and Mills had been mentored by someone in Jamaica who either worked under on learned directly from Bud Winter.
One thing that is different from the Bud Winter programs is the power work in the MVP plan. Francis has sleds once a week and 10X40m steep hills once a week, then two overdistance sessions. The power sessions seem to allow you to run the longer sessions faster over time.
The MVP version at least seems to work very well as GPP for Charlie’s s-l and you benefit from doing it for a long time (something like 3 months) as the Jamaicans seem to do.
Brauman’s training is a bit different.