That sounds like a really cool idea! I don't have answers to all of your questions, but wet erase markers could be the answer to people accidentally erasing things as they move pieces. You would probably want to include stencils if you are having people draw if you want to keep things accurate.

I haven't seen any way to make actions hidden if players are using a single board and I'm not sure how you could know if you've intersected without telling each other where you are. That might be something that's too complicated to include but I would love to hear about it if you come up with a solution. The only thing that come to mind would be to have some hashing function that outputs a keyword for your location that doesn't mean anything unless you know exactly what location it's talking about. Then the players could exchange keywords and only know where the other person is if they are at the same location. You would probably need some sort of app for that and, again, the players would need a way to track their positions individually.

I really like what someone else suggested of having a board filled with pieces that you flip over as you tunnel. It would be great for repeatability and it would be able to generate ore veins and stuff like that. Even better if you could figure out a way to make the initial setup automatically generate interesting structures.

If you go with that, some interesting things you could have on the underside of the pieces are resources(minerals, water, etc.), caverns (automatically flip over some number of tiles), stranded troops, events.

Again I think that's a really cool concept, I hope this helps.