I ran aground on a reef and am completely unable to move my carrier. The waves move above the propellers but they won't even turn. My entire game is softlocked because of this.
You have most likely ground the underside of the carrier on the reef. Low enough to keep the waves from going over the props but high enough to keep it stuck. Did you try using your side thrusters to shake yourself loose?
Suggestion: Maybe using a couple of empty barges could be used to pull carriers of reefs, this could be a time consuming process which causes damage to the carriers main hull and needs special equipment loaded into the barge in order to do this. Making the Epsilon vulnerable.