My first question for a client like this is, "Why do you want a thick slab of wood for your sign?" Is he thinking that it would look 'historic,' so that it would harmonize with the building?
In my mind, a 2-inch thick wood sign, especially with sandblasted graphics, is neither traditional nor historic. It is a modern treatment. Maybe hand-carved could be considered historic. In either case, the wood blank is not cheap, as you already know. HDU is easier to work with, in my opinion, whether sandblasting or carving. You can incise the graphics with carving tools, or have the graphics in relief. A bent spoon gouge used on the background can give a carved-out look. Still, is this not often a look that is more rustic rather than historic? During the years when everybody was sandblasting redwood signs, I believe it was often inappropriate for the architecture. We were doing it so much not because it was appropriate, but because it was new and different and we could charge a lot.
A point already mentioned to is that the panel does not need to be 2 inches thick to achieve a 2-inch-thick look. A thinner panel can be framed to give the appearance of thickness. A frame on the backside whether made of lumber or metal, can push the face away from the wall. Then a finish frame can cover the edges. You can get a thick look this way without the weight and the problems associated with a wood slab. Of course, HDU doesn't have any of the problems that a slab of redwood or cedar has, and it can last practically forever.
If this were my job my first inclination would be to suggest a glass smalts background and gold leaf graphics. Smalts is an old-fashioned, historic treatment that has a nice masonry look to it. Then add a decorative frame of redwood or cedar that would take a stain and still have a wood look without appearing rustic or like a 'state park' sign. The signs I have made in the past with glass smalts were on MDO panels (this tells you how long it's been since I've done one), but I would experiment with smalts on an aluminum composite panel.
My next choice would be an HDU slab painted to resemble marble. I would router a decorative molding treatment on the edges of the HDU, and then finish the face till it was very smooth before marbleizing. If you are not confident at marbleizing, some commercial painters are good at it. We have some in our area that can achieve a very realistic look and they don't charge as much as you might think. A marbleized background can be hand lettered or have flatcut letters mounted to it.
A digitally-printed background to resemble wood might look cool, as jsmoritz suggests, though it might not have the lifespan of the other treatments. You could even mount flat cutout graphics to it.
I think the letterstyle is important, too. It can look better if the letterstyle fits the historic look of the building. Not always, but sometimes, a historic building can look a little ridiculous dressed in Helvetica Medium, though I am not one of the Helvetica haters.
Brad in Kansas City