The difference between 2-node and 1-node has no “trainable” parameters. So to suggest that you’ll need to spend more time in the 1-node case tuning doesn’t really make sense.
With 2-nodes at the end, you can think of getting 2 sigmoid-ed scores, and what you do with those is up to you. A popular way is softmax of course, but if you have precision/recall constraints it seems to me you’re going to end up doing tuning either choice of architecture.