Are you using these?
I'd go with a bigger exhaust if you have it and here's my reasoning, if you have a bigger exhaust with a damper you can part close the damper to restrict the flow, if you have a smaller size you're stuck, and you can't open it out any more if you need more flow!
If you have damper on either the exhausts or on both of the feeder pipes, you can close down the fire, smother the coals and come back to the pit the next time and relight the charcoal that survived being snuffed out, if you don't have dampers in either the exhausts or the feeder pipes, you don't get the chance to smother the coals and you just have to let it burn out every time you use it, this can be quite wasteful depending on how much you are going to use it, and how accurately you learn to fuel it for it's cooking load.
The rain caps don't block the smoke and they are a good idea to help slow the flow of water into the pit when it rains.
Good luck take pictures.
Just a note about exhaust placement, on the plans above you can see the exhausts are below the grate level in the cooking chamber, this gives you much better burn characteristics, and allows the cooking chamber to function as intended.
If you put the exhausts at the top of the barrel it just doesn't work as well as it could, so look, think, the cut the holes, if you put them in the wrong place, either get another barrel and start the cooking chamber again, or replumb the exhaust inside the cooking chamber to the right depth to make it work.