After much checking, finally got this corrected. Due to mileage, the suspension bushings were pretty soft and fairly worn. When making turns, bushing compliance allowed just a slight amount of lateral movement in the front axle. When turning right, it would push the axle to the right and allow the front differential flange to contact a heat shield on the exhaust system. As the bolts in the flange rotated by, it would snag the heat shield, slightly pull it out and then allow it to snap back.

New bushings eliminated the slop, no more axle displacement, no more clicking.