The first thing I needed to do was to take out the brett so when I blended in the sweet brown ale the brett wouldn't chew up all the sugars and blow up the bottles. The author of http://themadfermentationist.com/ (also Oldsock on HBT) suggested he had good luck cold crashing and using campden on a sour beer before blending with a non-sour portion. Since he's quite the expert at sour beers, I decided to follow his advice.
On Thursday I put the one gallon jug of the sour portion in the fridge to cold crash it, the idea being to drop as much of the brett out of the solution. On Saturday morning there was a new, thin layer of freshly crashed yeast and the cake was nice and firm. I proceeded to rack the beer off the cake into the bottling bucket (I was running short on available fermenters to use). I crushed up one campden tablet and added it to the beer before covering the bucket with a fermentation bucket lid. Campden is often used in beer making to break down chlorine/chloramine from water sources but it is also used, mostly in wine production, to halt fermentation before the beverage gets too dry. Here, the campden is used to halt fermentation by brett. Campden mostly deactivates after about 24 hours so it requires some time before new beer can be blended in and bottle conditioned. Cold crashing helps reduce the number of yeast cells in the beer, making the campden more effective simply as a matter of the number of cells available to survive the campden treatment.
One Sunday evening I uncovered the brett portion and siphoned in the brown ale portion. The brett portion by itself was incredibly sour-smelling but when the two were blended it had a very noticeable Petrus oud bruin-like smell. Unfortunately the brown ale was under the full four gallons so I ended up with 4.5 gallons of oud bruin once mixed but that's still a good run. I bottled it in champagne bottles, just in case it starts to overcarb, and ended up with about 23 750ml bottles (I used some 330ml bottles I had).
My next -- and final -- post on this subject for the time being will be a tasting in a few weeks when I pop one open. I may revive this line of threads later in the year if I decide to do another batch and change things up, like adding fruit to it.