Unfortunately, they all speak the truth.
your idea, while wildly unnecessary, complicated and tedious (and thus perfect in every conceivable way)
Your dwarves won't path through the doors if they can't open them manually (without a lever/trigger that is)
Maybe once toady works out a bit more of the pathing mechanics.
It really needs to wait for a "path learning" dwarf object that.
And then we'll have fun trying waiting for dwarfs to explore the accessible map (especially fun when it's dynamic) before they'll start hauling back rocks dug out from the furthest recesses of the mines by other dwarfs. And the possibility of "hey, Urist, you know if you wander down there, there's a whole lot of tunnels with rocks in" 'communication'. (Moderated by relationship data, of course. "Hey, my good friend! I see you're into leatherwork, this season. Well... I was passing by a stockpile on the other side of that bridge, and guess what I found! A whole pile of good quality leather you can use!", or "um, yeah... sorry, forgot your name, but I'm a passing acquaintance of your wife. I've heard you've started a little 'project' in that Crafts Workshop. Yeah, yeah, all hush hush, I understand. Look, word on the street is you're looking for uncut gems. I don't actually know where there are any, lying around, but I've heard rumours of something interesting through that door over there. I'm a bit busy hauling wood to go and look myself, but it's probably worth a try. I'll let your wife know if I pass any on my travels, if we're having lunch at the same time tomorrow. And if you find any closer stocks of cut wood, I'm hoping you'll help me out. That darned woodcutter went over the hill to cut down trees instead of taking the ones growing just on the other side of the brook. Anyway, just let your missus know... Cheers, I'll appreciate it." )