Nutz:
Don't be afraid to mount a tang sight on the wood.
This was routine for small-bore competition back in the day, up to Olympic standard, and some incredibly tiny groups were shot that way.

The Greener tang sight would be "pukka" and they do come up for sale occasionally but are rarely offered complete with the aperture disc. The Parker Hale and BSA versions are fairly common however, especially in the UK.

Check this website for more information.

I should add that the base for the PH and BSA sights will most often have a concave underside contoured for the smaller Cadet rifle. A little filing may be necessary to fit it snugly to the full-size MH wrist, although a bed of stiff epoxy bog will do the same job and can be made to look invisible if darkened correctly.