Historically the difficulty isn't in building the mast, it is in preventing the airship from being smashed into the mast by the wind. Or in dramatic cases flipping end over end because it was only moored on one location.
Interesting. Why a mast and not just the ground? Pull up the mooring lines (probably more than the amount needed to actually hold the ship, for redundancy), connect them to the ship, then pull on the lines with winches until the ship is on the ground. That's basically how seafaring ships work... are there any unique challenges with airships?