One thing I do not want seen is random factor in trusting players with server permissions of any sort.
Better response, IMO - staff rank dedicated to nothing but cleanup., to be applied for and chosen in the same manner as mods. Duties to include finding and repairing or regenerating the locations, as well as answering basic questions (this should take a little strain off the mods, though I don't think that is a major issue ATM). Duties and permissions would NOT include anything that would infringe on moderator duties and permissions.
I cannot imagine that the owners would view a random pick or lottery being involved as desirable under any circumstances. Trust of this nature should never be left to chance.