On 13 November, the Jets placed Everberg on waivers with the intent to terminate his contract. On 14 November, he signed with EV Zug of the Swiss National League (NL) for the remained of the 2018–19 season. Everberg quickly adapted with Zug, regaining his scoring touch in contributing with 12 goals and 28 points in just 31 games. He continued his output in the playoffs, notching 8 points in 10 games. As a free agent in the off-season, Everberg opted to return to his roots signing a five-year contract with original Swedish club, Rögle BK of the SHL, on April 23, 2019. Everberg as a late bloomer, made his first appearance for Sweden at the international stage at the senior level of the Euro Hockey Tour during the 2016–17 season. He remained on the pre-tournament squad in preparation for the 2017 IIHF World Championship in Germany/France. Despite initially being left of the final roster for the Tournament, Everberg was later added and made his debut in an 8–1 round-robin victory against Italy on 12 May 2017. He scored his first goal, the game-winner and added an assist in a 4–2 victory over Slovakia on 16 May 2017. In helping Sweden capture the Gold Medal, Everberg completed the tournament scoring 2 goals and 3 points in 6 games. During the 2017–18 season, with the exclusion of NHL contracted players Everberg was selected to represent Sweden at the 2018 Winter Olympics in Pyeongchang, South Korea. Used in a checking-line role, Everberg contributed with 2 points in 4 games in a 5th-place finish.