The third image shows my first test. A hopper attached to the underside of a chest, filtering to the right into two other hoppers. The first of the three hoppers has another hopper below it filtering to a chest in front of it. The third of the three hoppers also has another hopper below it filtering to a chest in front of it. Items placed into the topmost chest will first filter downwards into the first of the two bottom chests. When the chest fills up, it will proceed to fill the attached hopper until it pushes items to the right into the hoppers attached to the right most chest. This will work for a generally large number of chests in the same setup. It will fill up chests from left to right if created in the same way (or right to left if making a mirror image).

In the first and third images, this setup is utilized in order to create a sorting system. The chests at the bottom are setup using comparators in such a way that they will only accept one type of item. A comparator is used to output a signal with a power of 1 by keeping 22 items inside of the attached bottommost hopper. When a 23rd item enters, it increases the power to 2, powering a redstone torch which powers the bottommost hopper. This allows items to exit the hopper until the number of items inside reach 22 once again.

The hoppers on top utilize the same system first tested, causing items to travel from right to left and was supposed to take the items matching the 22 inside of the bottommost hoppers and distribute them into the attached chests. However, contrary to the initial testing, all items bypassed the attached hoppers and traveled to the chest on the farthest left (used as a catch-all).

The second image shows the same as the first image, with labels.
1) The chest into which all items are placed, unsorted.
2) The first hopper. Inside is 22 stone, and is attached to the front chest.
3) The first chest. Is attached to the hopper labeled (2) and should catch stone.
4) The second hopper. Inside is 22 redstone, and is attached to the front chest.
5) The second chest. Is attached to the hopper labeled (4) and should catch redstone.
6) The third hopper and chest. Is a catch-all and has nothing inside. Should not catch stone or redstone.

The problems are this:
1) No problems.
2) Should catch stone, but does not allow stone to pass.
3) Should catch stone, but no stone is filtered.
4) Should catch redstone, but does not allow redstone to pass.
5) Should catch redstone, but no redstone is filtered.
6) Shouldn't catch stone or redstone, but all is filtered to it anyway.

If clarification is needed, an email can be sent and I will answer any questions as best as I can. I will continue further testing.