Once More Unto the Breach
Based on one of my favorite lightweight systems (Lasers and Feelings by John Harper), Once More Unto the Breach by Wouter Eilers is a direct and easily adaptable RPG about apocalypse survivors who slip back in time in order to prevent the end of the world. You have two stats, roll D6 in a clear under/over success/fail system, and are trying to pick up clues in order to prevent your timeline’s Ragnarok… but it might already be happening, or it might not be avoidable at all.
