Accies occupy second spot in the table, four points behind leaders Marr and a massive 25 points ahead of third-placed Jed-Forest, who have three games in hand.
That situation means that one point will be sufficient for O’Riordan’s men to build an unassailable advantage over the Borderers.
The Capital outfit, who displayed their battling qualities to overturn a 14-0 deficit in beating Dundee High 30-27 last time out, will focus on winning their two remaining fixtures – they will complete their programme next week at home to Aberdeen Grammar – and hope that Marr suffer a defeat in the brace of games they still have to play.
The Ayrshiremen welcome Musselburgh tomorrow.
The eventual Division One league champions will claim the sole automatic promotion berth, replacing Gala whose relegation has been confirmed.
The prize for the team that finishes second will be a play-off against the Premiership’s second bottom side, Hawick, to determine which club will compete in the top flight next season.