You should tamp with your forearm/wrist straight and upper arm parallel like this:
From HB Roadshow - Espresso Tamper ReviewsNotice he is not "palming" the tamper. If you grab the tamper like you would a doorknob, you'll naturally keep it straight. Don't grab it by the ball like you might a rubber stamp. If the tamp is canted, don't try to correct by retamping. It will only make it worse by breaking the puck/basket adhesion and further fracturing the puck.
You may want to try removing the portafilter basket retainer spring and tamping with the basket on the countertop, then gently sliding the basket into the portafilter. It's a fairly foolproof way of assuring the tamp is straight.