Mushiness is usually overcooking. I think your method might expose them to heat for too long.
I boil with shells (and head if heads-on). I get a rolling boil, using liquid crab boil, some powdered cayenne, a couple of bay leaves, and a halved lemon. Add the shrimp to the boil and leave them for about 3 or 4 minutes depending on what the water is doing (thoroughly orange is the best clue).
Then I turn heat off and immediately add a bunch of ice cubes. The point is to get the heat down quickly so the shrimp stop cooking. So you don't want to get the water cold, but enough ice to quickly get it down to lukewarm. Then I let them soak for about 20 minutes or so.
Try adding the ice after your boil cycle. It should get rid of the mushiness.