Shop or Mercenary room every 5th round
I think it would be nice to have an expensive way to complete comps, so once you have committed to a path you can't get locked out completely by variance, if you are willing to pay. Also, there could be a way to convert items into other items, for a cost, so that you can strategically itemize, for the cases you are deep in a comp but receive items that can't be used properly.
There could be an item merchant shop / mercenary shop, alternating, right after the each carousel room.
The cost of the items and champs could be based on the existence of other items/champs in the game (supply and demand). So if you choose something that isn't anywhere, it would be cheap, and if you want something there is a ton of out there, it would be quite expensive (but possible, for that steep cost)