The major restriction with the Martini Henry action is the length of the cartridge you can fit in the action. You need a cartridge that isn't so long that it won't "turn the corner" going in. The .375 Flanged will fit. I have never tried the .475 but I think those big 3.5 inch cases are just to long. I don't think the 500NE will fit either, but if it does let me know.

The other determining factor is strength. Made with modern steel the Martini Henry would be well up to the task with any of these cartridges. But absent any knowledge of the type of steel used in the MH, I would be reluctant to build a gun in the calibers you mentioned.

Have you looked at the Westley Richards 450 Musket No.2?