I've talked about the page solution before, but slightly different so stick with me here:

Under what I was proposing, all floors drop pages just like Savage raids. However, I would suggest that the pages are used to exchange for the items that drop in raid, and are dropped to your inventory after every clear with the restriction that you can only exchange pages from a floor if you have not already received a loot drop from that floor that week, and if you exchange pages for, say, a shaft, you now are locked out from rolls on floor 4 for the rest of the week. The system might be more complicated to digest at first, but would allow Square to not have to alter too much of the current system while adding in a sort of pity timer to drops. Say if you've fun floor 4 10 times and didn't get your drop, for example, now you've still got that shaft you needed without having to still keep running and hoping RNG favors you this time.