Hmm, I'd try the router approach. Probably need to play with the insert's to see which slot you need selected for the generator. (Insert top, front, bottom, side, slot number, etc...).
As for feeding the router... A filter wont grab stuff from the bottom of a barrel if you place it directly under the barrel? Damn. That'd be my first try. If that doesn't work, try deep storage unit from MFR. They can hold up to 2 gazillion of something.
Filter drag stuff out and directly into relay with 1 pneumatic pipe before the router (so the router isn't connected to your relay/filter/barrel. Trying to keep away from needing a machine filter that way. Need bandwidth and speed on the router too.
Damn, I gotta go try that barrel thing with the filter. I never needed it but had considered it a possibility for the future. Now may have to use what I just said instead.
P.S. - Filter needs a timer (redstone pulse) to trigger dragging of stuff out of a chest/barrel/etc... Did you have a timer?
P.P.P.S. - Why am I feeding into a relay and not directly to the router from the filter? Yeah, I'm scratching my head too, ya don't need to do that. Just filter to pneumatic pipe to router. That works fine. When router can't feed a generator, it will not accept any more stuff. And the filter will jam and no longer pull stuff from the barrel. Effectively stopping the process until the generators process more charcoal.
P.P.S.- In my last world I definitely had a barrel with a filter under it. You need a timer to get it to work. Also make sure you have the filter set up to where the + side it under the barrel and the o side it facing down to your pipe/relay.