Oh, I see what your getting at, the springloaded extractor needed for rimless and belted cases. Of course you are right...for belted and rimless cases.

Once you turn the belt off the H&H case you don't need the spring loaded extractor. A fixed extractor will work just fine. (Never worked on a Hyem so I don't know if it has a fixed extractor, it must because I see the .375 Fl MAG NE listed as one of the calibers it comes in.)

Keep in mind the H&H cases aren't in the truest sense rimless cases, they are rimmed cases with a belt. Once you turn the belt off they are back to being rimmed cases. The H&H rim is .523 in diameter, the head is right around .510

As far as pressure goes, removing the belt is not going affect anything. You will have a case constructed like any of the modern rimless cartridges. No different than say a 404 Jeff or .416 Rigby, except this one will have a rim and extractor groove. The head is going to be fully supported by chamber wall.