Whoa!!
I followed a link here from IllinoisCarry.com/ We usually discuss advance Concealed Carry in Illinois, but we enjoy the cool links like the one to this thread as well. Awesome work. And as to a name, I make a motion for "Bertha" (she's big, mean, and I sure wouldn't want to be on the receiving end of her rampage.)
As to the butt stock idea, here are my thoughts, take them as you will. Get you a thumb-hole stock to mount centered up. Get you a 1/4" steel or aluminum plate (your buddy with the MIG should have a torch set up) cut the plate down and round the ends, set this plate up to mount to the factory stock locations of each gun (joining them together, giving you your desired rear support). Then drill out in the center of this plat to mount your thumbhole stock. At this point (depending on how clean the plate comes out) either paint and stain where needed, or you could go down to your local auto parts store and get you some fiberglass to "blend" the plate into your newly center stock. The fiberglass wouldn't need to have much reinforcement since it would all be for cosmetic appeal. this would also allow you to return both 870s to stock since you are using factory mounting points.
I also vote for two bayonets. You may be able to fabricate a bracket to mount an AR upper rail in the center of this creature for your additional attachments. And as for the pump action....what do you think about a pistol grip up there? (fixed or fold down). And by the way, in case you couldn't tell from my rant, my brain is going for building one of these myself, since I did have my mind set on an 870 Tach 2 with a knox stock....but what you have created is much cooler!
Two questions though...1. Anything to remember to keep from getting nailed in the head with the spent shells out of the left side? and 2. I noticed in the beginning that you had issues with the shells getting caught up when ejecting, how did you solve this?