Well the good thing is that you have both identified the problems and the solutions. My advice would be to use partner drills. I share the habit that you have of going straight back when pressured. And sometimes I will lean back with my chin up. Or even worse combine the two!

I do a drill where my partner comes straight at me throwing light straight shots and I pivot or sidestep to avoid the attack and counter. I do about 2 rounds of this. I am still learning the mechanics of it, but I usually pivot or step to my right (im orthodox) and jab or L hook to the pit of the stomach and jab, or a counter right hand. Moving left is more difficult and I plan on working on that as well.

Another one I do when I get caught in a corner is shell up, come back with a 2-3-2 and pivot to the right.

Anybody do anything similar?