I evaluated the swatches I ordered and settled on Seattle Fabric’s 3-Ply SWB-Tex. It’s the closest thing to what I imagined in terms of weight and hand feel, and it’s essentially Gore-Tex as it has a PTFE membrane. Some of the other options were much lighter and supposedly just as waterproof, but I was skeptical of the durability.
To turn this into an actual pocket, a piece of fleece is sewn to the welt material on the inside. The original pattern did not have a pocket of this kind, so I made this up as I went.