You've probably collected some moisture in the caliper from condensation over this winter, especially if it was like our 7-month long record one here.

First thing: try pressing (hard) against the outside of the moving cliper to push the puck back in deeply. Then, use the adjuster screw you're describing to make clearance of 0.004" to 0.006" (with a feeler gage, or else 1/4 turn of the screw) between the inside puck and disc. This is the starting point. Then actuate your lever until it pumps the moving pad back out, and see if it will then release properly after you let go.
If not, you can next try bleeding the brake. About 1 time in 10, this will let the water droplets out before they corrode the piston inside and it will then work a little better.
If this fails, you probably need to replace the O-ring around the piston inside the caliper. These dry out over the years and lose their elasticity: they must grip the piston on their insides so they can pull the piston back away from the disc when the lever is released. When they get old and "wet" from moisture, the outer piston just slips through them when applied and it won't pull it back from the disc very well. This then lets the outer puck squeeze the disc, and the brake drags.
