One solution is making the Dungeon item rates progressive; on consecutive runs, your chances to get the next item should increase by x percentage until you get your next item, which would drop the rate back to its current 1/9 chance.

For the raid drops I think there should be a token system in addition to the loot chests. Get a token at the end of the run, and need an y amount of them to pick a specific from the loot table. It would make running for specific gear a lot better. I think there's been rumours about HS having some kind of a token system along with the normal drops, but they's just rumours until it gets verified.