It has to be said------this is one of the more bizarre projects, I have ever come across. It rivals the guy I met who was rehammering cymbals, with a claw hammer. Clearly , you need to realign all the lug placements, to get the snare bed to line up, or you could gently extend the snare beds, I suppose.
I would plug all holes in the shell with dowels, otherwise there could be such a pressure drop, you will think you are pounding a round steak, not playing a drum(you are likely to get leaakage past the wrap). Pitch is created primarily by the heads and the wires. If you want a cracking snare drum. Get thin heads and put 12 strand carbon steel wires on it. Whatever wires you use, check them for timbre. Some wires have a much higher resonant note. A lot of modern wires are made of crappy recycled steel in order to give that snareless throaty rap, so popular in modern music. It doesn't matter ,how many lugs you have, you will be able to tune a thinner head up quite well with 6 lugs. If you go to stiffer hoops----such as 6 lug cast( they are hard to find but they are around), there will be less flex in the hoop and the shell will have to take it all.. The greasing thing tnsquint suggested will help a bit but I think the nylon washers will compress a little and relieve tension as you are taking it higher----solid washers well greased, would be better. -----------I have a lot of 6 lug snare drums that tune really high, naturally----with factory components. I have sold a few, lately and had to get them down, to please the buyers.l had to take off original , mint, carbon steel snarewires and put thicker heads on to reproduce the hatbox sound so prevalent in modern recordings. Kind of the opposite of what you are after.