What is a “bag grip”? Are you referring to the Prince of Wales grip?
Actually, the 'Prince of Wales grip', a term generally used on British shotguns, refers to the degree of curve rather than the shape of the grip itself.
From ShootingUK:
What's the difference between the classy-sounding Prince of Wales grip and a standard pistol grip on a shotgun?
It’s all to do with the radius of the curve.
Most pistol grips having a curve of relatively tight radius, while the Prince of Wales grip has a very much more open curve.
The classic English double-trigger side-by side shoots and handles best for most people with a traditional straight-hand stock. That’s because the shooter is easily able to slide his trigger hand very slightly backwards, without materially altering his grip, when he pulls the back trigger.
With a single-trigger gun, which most modern
over-and-unders are, this is not a necessary requirement. The trigger hand stays in exactly the same place while both barrels are fired, so the grip can be at the most comfortable angle possible.
However, in the case of the
double-trigger gun, some compromise is possible, and some shooters find the slightly curved Prince of Wales handgrip more comfortable than the straight-hand stock, and still allowing for a slight change of grip between trigger pulls.
The Prince of Wales (the one who became King Edward VII) had his guns stocked in this manner, hence the name. One contemporary report records that, on a double-gun day, he had four pheasants dead in the air at the same time. That not only shows his shooting skills but the first class teamwork between the Prince and his loader.
One of the illustrations (and caption) from above article (there were two with 'rounded' grips and this):
The Prince of Wales-style semi-pistol grip is very comfortable in the hand. As featured on a Zoli Pernice.
Beautiful rifle but that was my first thought as well. I think a leather wrapped limbsaver recoil pad would be a good replacement for that steel buttplate.
I would advise against buggering that steel buttplate or any of the engraving. If it were mine I would keep it as 'original' as possible, yet consider adapting claw mounts to the already altered scope mounts that are presently installed. Fill screw holes with screws, no welding.
It is, indeed, a fine old Mauser sporting rifle.