Here's a mockup of what I'm using.
The chest on the right side is the dump chest. The adjacent filter (no items in filter) pulls a stack at a time from the chest into the router. The router has a bandwidth upgrade and a machine upgrade. Without the machine upgrade, the router will sometimes put items into the filters.
The second filter, on the left (no items in filter), pulls stacks of items from the router into the left chest for overflow. In my real setup, the filter colors the items for overflow storage and sends them back through the tube network.
The timer pulses every 0.5 seconds, first causing the left filter to pull jammed items from the router, then through the repeater so momentarily later the right filter inserts a new stack. If the incoming item has nowhere to go, it will sit in the router for longer than 0.5 seconds and get cleared on the next cycle.
With a large number of barrels, the router speed upgrade may help to make sure items get sorted within 0.5 seconds, but I haven't had any issues on SSP or SMP so far.
The benefit of this setup is that there is no need to specify which items belong in barrels in a sorting machine, etc. Every incoming item can pass through the router and be ejected without slowing down the flow.