I don't know of any production tires larger than a 345. However, if you can get enough people to buy them, many tire companies would probably do a run for you in the size of your choice. I bet you'd need 100 people or so to make it cost-effective, however. Try calling around. I talked to Nitto before about a custom run of 345-sized drag radials for stock Viper rear rims, and they WERE willing to listen, but wanted a pretty big order to make it worth their while.
As for the wheel, there is a good 1" of space you could use with a larger offset rim, and I think you could add 1/2" to an inch on the outside without it looking silly. So you could get about a 14.5-15" wheel on there with a little more offset and still look good.
BUT,
since no DOT tires exist in this size, you aren't going to find rims of this size either - so you'd be talking about custom rims and custom tires. In other words, VERY expensive. And without changing the setup at the front, you might very well screw up the handling of the car. And no doubt it would track the road a bit worse than it already does... AND you'd have to buy enough tires to satisfy you for life, or pay big bucks to get another run made.
My .02
