The cost of wood vs. stone veneer does have many factors to consider. The cost of materials is much greater for stonework vs wood but depending on the detail work in the millwork, wood could be much higher than stone veneer. but then again what type of wood? And what type of stone? I don't think your going to get any worthy answer here. not enough information and too many factors that determine cost. get a quote from another contractor when your GC isn't looking. An option would to take in both drawings to a contractor and get a price on both if will give you peace of mind, but knowing you are wasting someone elses time might give you another thing to fret over.

One of the things that gets me all twisted around in these types of choices is the historical context. The most appropriate choice from a decorative standpoint may not be the most appropriate choice from a historical standpoint. The most appropriate one may not be the one that looks better. But if you are changing it out of necessity, maybe letting the historical trump the decorative is kind of revisionist anyway because it's not really historical, it's a replacement. See how I can twist it around? But part of the issue is that in the US there is such little historical fabric. I was talking to a patient from England who said that the house she grew up in was 500 years old But as far as the interiors went, they did not necessarily pick a bathroom tile or fixture based on needing to look "appropriate" in a 500 year old house, because what IS such a thing? Here, we try to preserve each element because of its rarity, but when it comes to having to Replace, what then? Maybe if you are replacing it with something that was not there to begin with (I doubt there was a marble facing on the firebox on the second floor of a house like this) --maybe you can replace it with whatever you like. (?)

I think it will look lovely. That green is wonderful (care to share color?) and will look perfect and quite colonial with the brick. I am not sure about the beadboard idea, though. I would go with a smooth look like the one in your inspiration picture. I imagine you could have someone build the entire surround to cover the alcove or incorporate that alcove into your plan. Also, you seem to want to combine several styles: the rustic heavy mantel and the very formal 18th c. style going to the ceiling. Once you decide which you really like, everything will fall into place. I am betting some others here will come up with great ideas and maybe even pictures that combine both looks!

I'd suggest looking at houzz.com. You'll find lots of inspirational photos there...search on built ins in living rooms.