re: Welcome to the forum.
I have no fast, easy way to clean up your buttplate casting.
Were it me doing the work I would use various grades (or grit) of Silicone Carbide sandpaper to sand the plain, uncheckered areas down to obtain a smooth flaw free surface.
This sandpaper is commonly called "Wet/Dry" in the U.S. because the adhesive that holds the grit in place is waterproof. It is colored black but should not be confused with "Emory Paper" which is also black but has a much softer abrasive.
As for the checkering, I would use a 3 Point or triangular file to file each individual line of the checkering. This would maintain the typical 60 degree angle that most checkering is done with.
Jewelers files can be purchased and the bend that some of them are made with would be a benefit in getting into some of the small areas.
As for the attachment of your barrel, if suitable straight slotted set screws are not available for your purpose you could perhaps go to an automotive supply store and buy several high strength bolts in the correct thread pitch and size.
These are very tough steel but they can be cut with a metal cutting hack saw to a suitable length.
To form the slot, after squaring up the cut surfaces with a file use a 3 cornered file to lightly make a notch across the center of the end of the screw.
Using this notch as a guide your hack saw can then be used to cut a slot for the screwdriver.
If you have access to an electric drill, you can hold the short set screw you are making in the chuck.
While the drill is running, use a flat file to file the end opposite the slot to a 120 degree cone.
If the 3 holes for these screws are drilled while the barrel is in place, run the drill bit in until it makes a full conical impression in the barrels breech plug. This impression should only be the size of the drill and not actually create a hole in the barrels plug.
Screwing the coned set screws in until they bottom in the 3 coned impressions will not only hold the barrel in place by faying friction but the mechanical interface between the screw points and the breech plugs "impressions" will prevent the barrel from moving in any direction.
If you want the three cone ended set screws to do double duty, rather than actually creating the three cone points in the breech plug stud while the plug is mounted in the receiver, just run the drill bit in until it lightly touches the breech plug stud.
Remove the barrel and breech plug from the receiver and note the three marks.
Using these as a guide, make a dimple or dent using a center punch at each mark however, make it about 0,5 mm (.020 inch) closer to the barrel breech face.
Using these center punched marks as a guide, drill the drill point only into the breech plug stud.
Now, when the three cone point set screws are installed they will not only hold the barrel and breech plug stud in place but they will actually create a force which tries to cause the breech plug stud (and the barrel) to move tightly against the receiver assuring a tight joint for years.