I don't have speedplays, but Bebops which are similar. They are designed to be "step down" pedals. (I heard that somewhere.) It's one thing I really like about this style is the recessed cleat. I pop out and then move my foot forward so the pedal is essentially under my arch instead of the ball of my foot (where the cleat is). If you're slipping out, you're pointing your toe down, push down with the heel a little.

Do NOT tighten it, you'll not get out of it! (If the shop has them correct that is.)

Also, are you right leg dominant? You should be unclippping left so you can be ready to push off with the right leg. (Or the opposite if you're left). I learned this because I was taking 10 years at red lights. Unclip right, put foot down, unclip left so I can prepare my right leg to push off. My starting and stopping has gotten much, much smoother. When I'm rollling to a stop and I'm unclipped left and start chanting "left side left side left side" and by the end of the day, I'm doing left automatically. Cheezy but it worked for me.