Random notes on the process
Well, here it is 6 months later, and I'm finally making progress on this project.
I recently had all of the files printed out on cardboard stock (free for me...never a bad thing) and I have just started mounting them. I went to Michael's (a US based arts and crafts store) and, after digging around and looking at the available mounting options, I went with foamboard, primarily because it is thick and stable, but also easy to cut through with an Exacto style blade, which is important because of the precision cuts I'm making. I decided to forego the normal board and to instead just go with the Plateau module because variability is never a bad thing...hence, there are many very small angle cuts, hence, the foam board thing sounded good

So far, I have the Plateau pretty much finished up...I first cut out the plateau tiles, and then mounted them onto squares of foamboard. I then did precision cuts to get the tiles all cut out, including angle cuts from the bottom of the individual tiles so they line up properly. I am quite satisfied with the way the board looks at this point, and I'm relatively confident that it will actually stay where I put it without shifting around, which was a major consideration in the backing material choice.
The counters are going to be a huge pain in the ass, but I'm sure with some patience they'll come out equally nice looking and useable (I have people in my group with fat fingers, who have trouble picking up small bits...hence, foamboard again is far superior to my other options for counter stock).
For stones I picked up a bag of polished river pebbles for a couple of bucks, most of them are the right size to fit on the board, and I'm sure there'll be enough to play.
For a timer I'm just going to pick up a digital kitchen timer.
Still not sure how I'm going to store the thing yet though...all the foamboard means it's going to have to be a reasonably large box!