Here is another way to make an adjustable rear sight. Get a bolt big enough to self tap into the battle sight hole. You may want to drill the battle sight out a bit. Rather than butcher a good rear sight, get one of those L shaped 2 hole affairs, and drill out the larger of the 2 holes.

Using some lube and a wrench, work the bolt into the big sight hole, self tapping it.

Chuck the bolt in an electric drill and then round off the bolt head with a coarse file. Smooth finish with fine file or sandpaper.

Cut off most of the bolt shank with a hacksaw. Leave no more than a tenth of an inch of threaded shank. Just enough to screw a bit through the sight.
Drill a 1/8” hole through the bolt, to act as the new rear peep.

Drill the hole way off center. Counter sink the front of the hole, slightly.
Blue the bolt.

By rotating the bolt in the sight, you have about 5 to 10 minutes of adjustment in any direction.

After rifle is zeroed, LokTite bolt into position.