Kind of a bit of a bigger suggestion would be to adopt a "storage and combine" system like a lot of autobattlers use (usually it's 3 level 1, become 1 level 2, 3 level 2, become 1 level 3, etc. - or in this case "common -> rare -> epic")
This would result in a lot more strategic thought when picking items/characters - as you could stash stuff away to get an upgraded version of the item or character later.
This would need to come with a storage system of some sort, so people could hoard these things and upgrade them as they go - and would give more complexity and progression to a run outside of "waiting for the epic"
Would also likely be easier to integrate into the longer format that an overworld/story/etc. bring to the table (even possibly letting you have different ideal teams for different regions/enemy types)