Brake pull - will hardware fix?

[D13]

87 1/2 ton 6.2 auto. Had a brake pull, could feel the caliper hang, snap to engage, then hang for a second on release. It's been sitting for a year (with diesel at $4.79!!), but now I need to start driving it again. Now, both sides are doing it (of course, not simultaneously). You hit the pedal, poor braking, then SANP as it breaks free, and lots of brakes. After the stop, you can feel the drag, until they pop back free.
In your experience, will the hardware kit alone fix this, or am I most likely going to have to do the whole thing? One of the calipers (the non-sticking one) was only a few months old when this started, so I would suspect that the pistons are not stuck in the calipers, and it doesn't seem to have any drag once they pop back, so i suspect the hoses are OK.

BTW haven't done square body brakes ever, even though my family has owned one since 1982. Are they similar to large cars of the era, i.e. bolt and sleeve?
Thanks!