Performance-based roll system

[Shurrikhan]

The only viable solution I can see, is that if the party consists of enough people who have run it multiple times, then the raid actually drops more loot.

This. More or less. At minimum, it will take half as many runs as there are players -- total playerbase, not just one party -- who wish to get an item, not counting remainders unable to form a party. At most, it will take the same number of runs as there are players -- again, total playerbase.

You increase the loot, you decrease the required ratio of runs.

Now, you can do this in a couple ways. It can be a literal increase (chance at a bonus chest), or you can include some sort of token currency per run such that one is able to generate further loot (i.e. cash the tokens for a reward of their choosing).