It might be a good idea to leave the dungeon chests in there, and make dungeons (and mineshafts) rarer and significantly more dangerous. Storage will still be very limited, and theres a nice reward for players who take the plunge (assuming they come out alive).
Theres a lot of options available for tinkering with monster/dungeon difficulty and rarity.
Also changing the mining level of stone/cobble/chests ect should help prevent players from 'cheesing' your pack's mechanics.