Rule number one in my book is to evaluate the barrels first. What are the wall thickness for your barrels? If they have decent thickness then the project is possible if too thin hang it back over a fireplace. If the barrels are thin or have deep pit stop while you are ahead. Is the gun on face? If not stop while you are ahead.

Can you shoot a short barrel gun well? Hate to spend thousands and have a gun that you do not shoot well. And this project will cost a lot of money if you are not doing the work yourself. Short barrels are different to shoot and tend to be very fast swinging.

You could have chokes added back to the barrels. A permanent soldered set of .015 and .030 would give that gun a very workable set of chokes. Please refrain from screw in chokes. they just are not kosher in a fine double to most of us.

The trigger guard can be tig welded if there has not been loss much metal. It will take time and money. It you end up with a major gap tig welding it will be harder to do and hide. I am sure someone here knows a person who could "bridge" the Atlantic with a tig weld but you it most likely look like crap. I have seen repairs that were tig welded that were almost impossible to detect. Might just be ahead of the game finding a take off trigger guard or making one from a stock trigger guard.

The stock looks to have been repaired to death. I would repair it to be used as a pattern. I would also replace the fore end. You will be surprised how much that will cost. Such a little thing is a hard to fit thing that requires a lot of time. And time is pure money on one of these projects.