Been a while since I did this.
R of A from a moving base: apply a false wind opposite in direction to the velocity of the moving base.
If your aircraft carrier is moving N at 20 knots, assume that it is stationary but that you are being affected by a northerly wind (ie from north to south) of 20 kts. Do all your calculations (E6B, pencil & paper, whatever) using this false wind.
If you know exactly what your endurance is, you can use the same technique for an alternate base. Calculate the distance and direction from alternate base to actual base, divide distance by endurance in hours, and use this as an assumed (or false) wind throughout the radius of action flight.
Hope this helps.
O8