I have seen this before. Very high levels of pectin in apples can cause clumping of the sediment when it sits for a while. My local apple farmer listed a few types of apples very high in pectin that he will not use in his cider because of this, but I can't remember if Staymans were on the list.
Try boiling a few ounces of water and adding a tsp pectic enzyme to the carboy. That should help break them up and settle them out if you are trying for a clear cider.