My first commute with clipless I must have unclipped 200 times... whenever I slowed down, whenever I stopped, whenever I thought I might have to stop, whenever I even thought about stopping, and just for practice...

You can practice by finding a safe stretch where you won't (probably) have to stop, and just clip and unclip, pedal a bit and repeat, over and over. Pedal, unclip and stop, pedal, unclip and stop. It does become second nature, and you don't have to fall over many times. Maybe you've already "done your time" on the ground