Well I was gonna suggest you loosen the tension but then you said you did that. Did you get mountain bike shoes? Mine are just like sneakers (recessed SPD cleats), I had too many near misses walking into convenient stores. The first and only time I went on a group ride, my friend said we are stopping now, I did and fell over. Haven't fallen in years... but I talk myself thru the stop with one word clues even now.
Couple weeks ago I was at the LBS and my mechanic said take it for a spin in the parking lot and see if it's ok. I did ... no shorts, no shoes and all I can say is weird. Kept thinking I was gonna fall off.
I would suggest dual entry pedals, just means one less thing to think about.
Practice practice practice