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hwally,
Welcome to the forum. You will find lots of helpful guys here and can get good advice on building the gun you really want. As stated above, you really need to watch the overall weight of your double rifle, otherwise it will be too heavy and clubby to use. That means that you will either have to buy, or have access to the use of, a metal lathe for turning down the sleever barrels and for boring out the monoblock.
One of the better ways of holding down the weight of your new double is to build it on a 16 gauge or even a good 20 gauge frame, if you can find one that is both strong enough and cheap enough to use. By general opinion, it seems that we have mostly decided that the donor gun needs to have a third fastener as a saftey factor. That is usually built in the form of a barrel extension that is attached to the top rib and extends back into a notch cut into the frame. The extension has either a slot or a hole through it, depending on the type, that acts as a third locking bolt to help keep the gun closed.
You need to spend alot of time considering various donor guns before you start. Generally, the more you can spend on a good donor gun, the better and easier the built rifle will be. Also, be sure that the barrel blanks you intend to use will be large enough at the breech end so that you have enough material for a smooth transition to the monoblock. That may sound simple or silly, but many barrels are not fat enough in the rear end to use as sleevers.
I don't know what you consider a "cheap double", but you need to understand that there is alot more work and expense to building one of these than simply plugging in two rifled barrels into a shotgun monoblock. These are considered "cheap" only when compared to a factory made double rifle.
Other things to be considered are : 1. Are you going to restock it? 2. Do you want a cheekpiece on it? #. 3. Is the donor gun in good enough shape that it will make a rifle that looks good and is dependable? 4. What kind of sights will you put on it? 5. How much time and money can you afford to invest in this project? 6. Are you capable of doing all the work on it yourself? 7. If not, do you have a machinist who will do it for you, and and what cost?
Good luck with your project, I hope I haven't discouraged you from doing it, but you need to carefully consider all your options before you start cutting up a shotgun.
Bob H.