Not sure how often guys flipped to be fully "opposite" what they were, but there have been several players throughout the years who have had to make major adjustments to how they play the game.
Ron Wilson comes to mind: he was a small, speedy, skilled center who spent three years in development with the Habs' farm team the Nova Scotia Voyageurs. He joined the completely gutted Jets in their inaugural NHL season in 79-80 and found himself in the position as their number one center, driving offense on a line with Morris Lukowich and Willy Lindstrom. Wilson was a smart player and can maybe be thought of at the time as a poor man's Martin St. Louis - he was crafty and able to use his smaller stature and quick movements to set up plays in the offensive zone. BUT he was ultimately punching way above his weight, as his offensive talents were simply not of the calibre needed to be a true top 6 forward in the NHL.
Eventually, with the emergence of Dave Christian (later replaced by Laurie Boschman), Dale Hawerchuk and Thomas Steen down the middle, Wilson found himself back in the minors by 81-82 at age 25, and spent the better part of three seasons in the CHL-AHL after two seasons as a top 6 center for the team..
At some point he must have been told by the team, or figured it out for himself, that the only way for a guy like him to keep an NHL job is to become a fourth line checking center and penalty kill specialist. Ironically, defensive-minded coach Tom Watt had not seemed to envision this role for Wilson, but when Watt was turfed new coach (and former teammate) Barry Long started playing Wilson regularly on the penalty kill unit alongside Doug Smail.
It took him a couple of seasons to fully stabilize in his new role, but by 86-87, at age 30, he had emerged as one of the best 4th line checking centers in the league, known as a good faceoff man and an effective PKer, with John Ferguson loudly beating the Selke drum on his behalf. He was able to use his size and speed to his advantage, particularly on the PK, as he could get in close and strip the puck from his opponents, and was adept at moving the puck up the ice on the PK, and getting back into the d-zone quickly if the play shifted.
As he aged, he found himself back in the AHL for a full season at age 32, and it looked like his career was coming to the end of the line, despite the fact that he put up 92 points in Moncton. At age 33, he was dealt to the Blues mid-season, and he was recalled immediately and given a job with the club, and put up 20 points in 33 games, his best offensive effort since 81. He had the full confidence of coach Brian Sutter and at an age when most guys from his generation were done, Wilson reinvented himself again as a versatile two-way player who could play up and down the lineup and slot into any forward position, playing both checking and complementary scoring roles, much like the Blues captain Rick Meagher, a speedy two-way player who won the Selke in Wilson's first season with the Blues. Meagher retired the following year, and Wilson stepped up and took over his role and played a solid three seasons for the Blues. He had one final campaign in 94 with the Habs before hanging up his skates for good at 37.
Definitely one of the oddest career trajectories in NHL history.