The problem I see if you jump from one instance to another is that the data directory may/will become inconsistent.
When you run your instance on your Linux, you’ll write data in your Linux data directory, but not in the windows data directory.
And vice versa.
So both directories will diverge.
Disclaimer : I’m not a dev, and don’t know in details how this is done.
If I were you, I’ll try the transfer in a one step one-way process.
Only go back if something doesn’t work.
And only start again making offers and trading when the transfer is definitely ended and well ended.
(avoid acrobatics, generally it ends up with issues.)