I learned from horseback riding to tuck and roll (or at least tuck). Don't try to catch yourself. Sometimes, you may wind up hand-down for whatever reason, but don't brace yourself and be rigid if that happens. Just go fingers to elbow to shoulder to back if you can. It's hard to do when you do the slo-mo topple, because you think you can catch yourself--and your bike, but it's not usually like just tripping and falling.

I wouldn't get into the habit of unclipping both feet to stop. That makes getting off the saddle difficult, and it's really hard to keep upright if you're putting your feet down while you're still seated, unless your saddle is crazy low. Generally, it works if you unclip one foot early, hang it down to the side, slow down almost to a stop, then as you stop, lift off the saddle with the clipped in foot (in the 6 o'clock position, where that's at the bottom), drop onto unclipped foot, and point the front wheel slightly towards the side that you keep clipped in (meaning the bike will be less likely to lean to the wrong side). I don't know of a lot of traffic situations where you'd be able to rely on unclipping both sides and doing whatever maneuver you have to to get stopped and off the bike. Practicing stopping this way won't be any harder than what you're doing.

Be sure your pedals are set as loose as they can safely be while you get used to it, and start out unclipping well in advance of a stop or potential stop. I used to unclip going towards most intersections where a stop was likely (I have those pedestrian counters that help), then I'd rest the cleat on top of the pedal and continue going that way. If I was going to make it through, I'd clip back in. If not, I was prepared. Eventually you get more comfortable with it, but sometimes stuff happens anyway.