I hate to say it, but the way you originally posted that made it sound like you wanted it to apply to Normal dungeons.
As for your response, yes, simply adding a Challenge Mode equivalent would help. Heck, SQEX alreay has a "minimum ilvl" option, all they'd have to do is determine "bronze", "silver", and "gold" times for each dungeon when run at minimum ilvl, and add rewards for each (a static extra reward once/week just for completing with "minimum ilvl" enabled, and better rewards like exclusive cosmetic gear and mounts for faster completions). That, and actually tune the dungeons to the minimum ilvl properly (so that they're a decent challenge at that ilvl).
It wouldn't be as good as savage dungeons (think Mythic+ from WoW), but it would be a start. :)
--Erim Nelhah
