May's only appearance of the 2011–12 season for St Johnstone came as a substitute on the opening day of the season against Aberdeen at Pittodrie. With appearances limited he was loaned to Alloa Athletic until the end of January. He made his league debut for Alloa on 10 December against Queen's Park, going on to score his first goals on 2 January 2012, netting a hat-trick for The Wasps in a 3–1 win against East Stirlingshire. After one month at the club, May had his loan spell with Alloa extended until the end of the season. May was awarded the SFL Player of the Month, Young Player of the Month and Irn-Bru Ginger Boot awards for January; the first time that one player has won all three player awards in a month. He scored four goals in the 8–1 victory against Elgin City that clinched the Third Division championship. At the end of the season, May won the Irn-Bru SFL Phenomenal Third Division Player of the Season. May signed a new one-year contract with St Johnstone.
On 29 August 2012, he joined Scottish First Division side Hamilton Academical on loan until 31 May 2013. May cited moving to Hamilton on loan, as "get his own career back on track." After four games without a goal, May scored his first goal and then another in the match, in addition to two assists, as Hamilton beat Airdrieonians 4–0 on 11 October 2012. After scoring fifteen goals this season, May scored two consecutive hat tricks, against Airdieonians, in a 5–0 win on 11 April 2013 and another against Livingston, in a 3–0 win on 18 April 2013. For his performance in April, May was awarded the Irn Bru player and young player of the month in the Scottish Football League. At the end of the season, May says he enjoyed his time at Hamilton. At the end of the season, May was awarded again when he won Irn-Bru SFL Phenomenal Young player of the Season. His future at St Johnstone appeared to be in doubt, but he signed a new one-year contract in May 2013.