I assume airships aren't allowed to touch the ground because it needs to rotate with the wind. For an LZ, the load could just be slung then released. If the craft jumps skyward, who cares because it can't land yet anyway.
To your point about weight, I was thinking that instead of permanent anchors fixed to the ground, you could use water bladders or those large military sandbags[1] for ad-hoc purposes. You need to forage for the ballast on-site because of the relationship of lift you described.
[1]: https://en.wikipedia.org/wiki/Hesco_bastion