Canvasback,
Welcome to this forum from myself and all the rest of us. First off, before you decide to convert your gun, we need to know what kind of lockup it has. Does it have a Greener crossbolt, or does it have a hidden third fastner? Those are two points that need to be considered before making your decision. An 1895 era gun is not the best choice for many of the larger calibers, but you could do a lower powered conversion on it if it meets certain other criteria. One thing to consider is that if you monoblock this action and insert new sleeved barrels into it, the monoblock will look somewhat different than the barrels when the whole thing is reblued. If you put full size liners through the existing barrels, you will have the same damascus look but it will mount and swing like an 8 foot 2X6.
Action size does determine the weight of the finished product to some small extent, BUT, your gunsmith should be able to adjust that a lot by the thickness of the barrel profiles. If the barrels are thinly profiled, then a HOLLOW wide rib might be called for. 12 gauges are not just good for 500 Nitro Express caliber sizes. I have built 45-70 conversions on 12 and 20 gauge frames both. The lightest 45-70 on a 12 gauge frame weighed 7 pounds, but it had lightly profiled, short,(20 inch) barrels. I have also done a 20 gauge bore rifle on a 12 ga. frame that weighed less than 8 pounds with 24 inch barrels.
If you are serious about doing a conversion, buy the book "Building Double Rifles on Shotgun Actions" by W. Ellis Brown. Read it twice, then understand that his book is just the starting point, you will still have to do a lot more research. Stay in the low intensity cartridge list.
Once you get a good idea of what is needed, then you will be better prepaired to make your decision. If you do go ahead, the book will make an excellent guidebook to guide you along the way, and if you decide to drop the whole idea, you will still have the book to read or resell.
Books are cheap, double rifles are not. Good Luck with your project. Bob H.