My river birch is one of the few trees that grows well here in South Georgia, and is very pest resistant and cold tolerant so I wish I had more of them, but they are expensive. One of your early writers explained how to grow a conifer from seeds in the cone. They talked about harvesting the cones in the fall and mimicking a three month winter. I live in South Georgia, and both my pine trees and my river birch are just now growing cones. The river birch cones are tiny, green, thimble sized, and eventually fall off and die, with no trees sprouting from them ever. (nature’s way). Why did your prior writer describe huge differences from mine?
Those are not mature, therefore, are not ready for harvest. They have to be brown and brittle. They will fall off at the touch when they mature. This does make it difficult to collect viable seed, since the wind takes them off with ease. It may be best to collect any casings on the ground near the tree.
The next thing to consider will be you zone. Zone 9 is the very edge of what it can tolerate, heat-wise. This will mean that your mild winters will make it difficult to fully stratify them. This means very low germination rate. The refrigerator will be your best bet for at least three months.