[Drew Hause]

Here is a 1910 catalog listing for decarbonized steel barrels

The buttstock has been replaced, then cracked and repaired.
I would strongly suggest cleaning off the rust and hanging it back on the wall; it is likely to fall apart with the next shot.

BTW a restoration video; but for the later model "Diana Breech" Davis with a pull-off FE

 

[Drew Hause]

It dates to after the crossbolt rib extension lockup was discontinued prior to 1902, and I believe is a BS (steel barrel).
This is Researcher's catalog page from 1922

I believe you are making a wise decision.