Any neck with 12 strings is tough to keep true long term. I had a friend who had a Carvin like this:
http://www.carvinmuseum.com/decade/images/93-doublenecks.htmlIt was a great instrument, though some people think otherwise. From what I can tell, they do still make them special order, and might be able to get you somethink like what you want.
I assume from what you are saying that you are looking for a 12 string acoustic (Dreadnought) sound. A guy in my band uses a Digitech pedal for an acoustic sound with his Les Paul for one song where the switch happens fast from electric to acoustic. It actually sounds pretty decent. I am not terribly impressed with those guitar synths. Get individual pedals that do just what you want.
I have an old RP-7 that has a 12 string setting. I played my Martin 6 string through it and it did sound like 12 strings and sounded awesome. You can get one of those on ebay very reasonable. Plus it will do a lot more. There is one on there right now, in fact.
I think you might do best getting a pedal board and building your own pallet of custom sounds for what you want to do. For my strat I use a board with a bunch of pedals then a Line 6 Pod X3 live. Sort of the belt and suspenders approach, but I sound how I want.
What kind of a sound are you looking for in your amp? I can't really tell.
Best of luck!

Kristi