this should be obvious enough: this cannot be achieved without using the save room. if the save room didn't stay the same after death, this would be a much harder game, and it could never become unwinnable.
so first off, don't try to exit the tutorial. just hop over to the secret zone, then ignite a warp bomb and teleport yourself out holding the master key.
now that you're at the save room with the master key, you want to avoid any chance you have at opening the village door, or getting more master keys. why?
well, the village contains all the main keys, and if you obtained access to it there would be nothing stopping you from going into the main doors and collecting all the ZUG keys; which would make both endings possible again. this is the same with the master key, because if you farmed it enough you would have no excuse not to unlock all the doors. so do not open:
-the O door, because then you can always just go back for more master keys, and you would be able to open all the doors.
-the G door, because it has a back entrance to the village.
-the E door, which contains the G key, allowing you to go to the village.
-the A door, because that leads directly to the village...
THIS is where it branches off from the ViL challenge. normally, you would open the O door so you can go back and master-key the rest of the doors (excluding A), but now that you wasted your master key on a non-O door, there's no hope in continuing the game without going to the village.
also, being opened up to the vault ending is not an issue, since you only had one key and one door to use it on. the vault ending requires at least two doors open.
our final obstacle is the A key. it enters into the stack as soon as we insert our first animal into the lift, so we'll need to either:
A. make sure it can never spawn in the first place, or
B. get rid of it while it's there
solution A is a little more complicated than B, and we can only nail it if we opened the Z or U door with our master key. the Z/U zone has no animals in it to start, so we wouldn't be able to pick up any more if we lost ours in there.
to perform this solution, just go into the Z/U zone, then drop all the save room animals in there and "reset puzzles" (or just take a warp bomb, warp the gun out, and shoot yourself with it).
all the animals that you may have had are now gone, and there's no way of getting any more.
or, solution B: redeem an animal, then throw the A key outside of the save room and "reset puzzles." since it came from the save room, it will never respawn.