Sorry but I think you are putting too much thought to a potential problem that probably wont exist in your lifetime if you are concerned about the inner crossmember corroding.
I`m not saying they don`t rust but I don`t recall any of the dozens of minis I have worked on or the 60-70 odd that I have owned ever having issues other than the ones with no floor pans and a tree growing up through them :).
The inner / outer sill box section is another story. my personal option is a light whiff of zinc on bare surfaces followed by a light corrosion inhibitor.
The original foam filled sills seem to have done a good job of keeping moisture and oxygen out. An open vented sill needs to breathe and it can`t do that with layers of paint on top,
My 1990 Rover Cooper still has its original sills in A1 condition, all I did was empty a can of chain lube up each one when it was a couple of years old so thats 26 years of research in my book.