Tubes can be attached to the top to put stuff in. Attaching them to the bottom gives you only this "You can store 1 stack and only 1 stack of stuff into a barrel through the bottom" I don't know what good that would do you.
As for a router system. You want an item-filter and tell it to only deal with barrels. You want to insert into top sides of the barrels. You want the bandwidth upgrade and speed upgrade.
To clear jams put a cobble structure pipe on the side of the router with an autarchic gate set to emit redstone signal if inventory empty. Above the gate put a timer set to be stopped while receiving a signal. Set the timer to 4 seconds. Above the router put a filter. Above the filter put your tubing to your chest for the overflow. This will automatically clear your jams. Or you could program a turtle to do it as well.
Seeding the barrels is needed otherwise the router will spread your stuff to the four corners of the globe (barrel room) with seeming little organization.
The thoroughness upgrade is of no use for this, and can be left off. It doesn't do what you think it should do. But it is working as it should.
I recommend you get 1 barrel with 64x64 of cobble, dirt, gravel and then if your using pneumatic tubes - put a filter before your router that intercepts those items and dumps them off to you kill room (lava, crystal, cactus) or your recyclers.
After finishing my room last night, I decided next I want my overflow chests to actually be hooked to an AE system that will store my less used but still useful stuff. Perhaps with a chest that when filled powers up the AE system and when the chest is empty, powers it back down to save power. But I got to get more crystal for this.
Also looking into deep storage for possibly dirt, gravel, sand, coal, charcoal, oak since I get a lot of that stuff but don't need immediate access to it.
Have fun!
