As a person who has built doubles using shotgun actions, please allow me to respond to your question with more information than you asked.

First, the BSS action was used by Butch Search decades ago to build double rifles and I have not heard of any failures with these actions, and I have read that in some of his later double rifles that he built on the BSS he added a "dolls head" extension from the barrels into the top of the action to hold the barrels more securely upon firing the rifle.

Your shotgun barrels would be used to make the double rifle barrels, generally.

Having said this, my recommendation to you is to purchase one of the well made less expensive double rifles such as the Rizinni

You will then have a double rifle that was built on an action proved and proofed to be used with large bore double rifle cartridges and importantly will be much easier to sell later in your hunting career, if you decide to do so. The Rizinni double rifle can be purchased at a discount below the retail price. A year or so back I was talking with a Rizinni shotgun dealer and he told me that another Rizinni dealer (Gun Sport in Odessa, Tx) had sold a number of these Rizinni double rifles and that the purchasers had been well pleased with them. I recommend that you call this dealer in Odessa, Texas and talk to him about these rifles and if he is like a typical "good ole boy" Texan he will likely give you a contact of a person who has bought one, if you ask him. Note: I can say this because I had the good fortune to live, work and hunt in Texas for 8 years--what a wonderful country to live in.

http://www.rizziniusa.com/double-rifles/rhino-express

There is another Italian double rifle of lower priced in the market--the Sabatti, but it reputation has been questioned in the market place, and therefore the purchase of one unless it is a give away price is not something that you may want to do. You can find all about this issue by search the WWW.

Of course, there is the used double rifle market where any number of large bore double rifles can be found at a reasonable price as the the double rifle market is a bit stagnant at present.

All-in-all since I gather that you cannot build a double rifle on a shotgun action yourself but would require someone to build it for you, you will be better served, satisfied and financially better off to do as I propose.

Kindest Regards;
Stephen