You can not have *ANY* splices or boxes burried in the wall - all have to be accessible. If you move a box, you will either be lucky and move it to the side where you will have extra wire or more likely will have to rerun the wire from the previous box or from a location where you can add an accessible box (attic, crawlspace, inside a closet). Either that or leave the recepticle in place and run a wire over to the new one.
As for the subpanel on an old fuse panel, it may be fed from one of the branch fuses in the main. You can't just put larger fuses in the main block. The panel has a max limit and it also depends on the size of the feeder.
The best way to clean this up would be to either replace the fuse panel (and service) with a new 150 or 200A service or at least put in a new service and feed the old fuse panel as a sub-panel (splitting neutral/ground in the process).
