I was a bit confused by your response wording above - it had me wondering if I was possibly doing the migration....don't know why it came across like that, it just did....anyway, going by info elsewhere it seems MDD does the migration ( even if it's a laborious one like mine might be ). So I'll run with that.
Joomla is currently in a transitional period of versions. Versions that are total rewrites of the platform so it's a migration rather than an upgrade. I don't want to risk complicating things with a migration of versions along with a migration of sites ( as well as the control panel differences that may or may not mean extra care ).
Firstly, I would like to get away from the current webhost, especially given recent circumstances. Move to somewhere I feel I might be able to trust more ( like MDD ! ).
I'd like to be able to do it your way but I think I'm going to take smaller, ( simpler, less risky ? ) steps, one thing at a time.