Hey man, how about this as something easy to try? Hopefully your barrel isn't too big a deal to remove. If that's the case this is a pretty simple thing to implement to see how it goes.
Cut a 6" hole in the barrel as low as you can and plumb an exhaust bypass straight into a T in the bench exhaust. Put a damper in the bypass. Start up, heat up your chimney, slowly shut down the bypass to get flow through the bench. By closing it incrementally you should be able to control chimney temps, speed up flow through the bench, and fix your condensate issue. Put a kitchen thermometer in the stack so you can get a good idea of exit temps, up at the thimble, and keep it above 220° or so. Put the whole bypass at the surface of that existing cob work so you can cover it with a bit of cob for sealing around the barrel exit.
You might even get hotter bench temps this way.
I dunno, just a thought.