The assumption that I have regarding the levels below ultimate is that they will drop a fair amount of R enhancement mats for you, because the designers want players to simultaneously be able to farm mats (to a degree) and actually strengthen in order to move up to the next level.
So I think that you're getting R enhancement stuff instead of silver mats from the silver chests, right? Use them. After a while, take another shot at standard. Once you can handle standard, farm that until you can handle expert. Repeat again until you hit ultimate. R enhancement stuff stop replacing silver mats at ult (though SR enhancement stuff still show up).