A couple things....
First, there's a thread up in the stickies on"Building A Lupara" that may provide some good input.
Second, as someone has stated, make sure you're not butchering a national treasure. That Parker in the pics lost $1k or so off the value when the hacksaw got busy. Or, doing something with a family gun that another family member may not want to happen to your mutual heritage.
Third, once a suitable candidate is located, be loath to prune the barrels to a mere 18 and skosh inches.A SxS with say, 25" barrels is shorter than an 18" barreled 870 with similar LOP, and that 870 is hardly overly long and cumbersome. And longer barrels handle much better.
Were I doing this, and I may at some point, I'd look for either an old Savage/Stevens 311 in 12 gauge, or one of the inexpensive Spanish 10 gauges imported a few decades back.
I'd cut the barrels just behind the chokes, get a good smith to do the forcing cones, and hog enough wood out of the stock to balance it around the hinge pin.
For the Spanish gun, I'd either cobble together some 2 7/8" old style loads or get a drop in set of 12 gauge adapters from Briley.
In either case, it would be a fine tool and fun toy.....