Vall, you can fix that without modification using a lace on leather should sling butt piece and then as many laminations of thick leather as needed to fill out the crescent contour. Di do this for an old Marlin 95 and a Sharps #3. More to get some length than to overcome the crescent, but it has that effect anyway. Quite easy to shoot.
Or you make a second stock for it of course...
Here's a picture of my Perfection's early Brown style buttplate.
If I was to build up the depth of the crescent it would easily add 1" to the length of pull. And then add a lace on cover, and I'd be stretching to reach the trigger. My only option would be to make up a 2nd buttstock with a plain shotgun style buttplate, or keep using this one with my PAST recoil pad, which is marginal at padding those points.
I do have a couple old crummy Ballard buttstocks I could refit to this #4 to use it in our 1000 yd. matches. But likely I'll just set it aside, and switch to my Whitney-Laidley .45-70, or my Hepburn in same. Both lighter guns, with 30" barrels, but more comfortable buttplates. Don't really want to change this #4, as it's the first Ballard rifle I ever bought many decades ago.