There's simply no way wind driven rain or snow could put 15 gallons of water down your flue.For a 12x12 flue, that would be more than 24 inches of rain, perhaps 20-30 feet of snow. Even with no cap at all, you couldn't get that much. What you show in your flue and fireplace looks possible from driven rain, not what you say you got in your ash pits.
Rain water penetrating the structure below ground level is a much more likely cause. In my old house during severe thunderstorms, I could get a jet of pressurized water squirting into my basement through the water pipe penetration which was 4 or 5 feet below ground. All it took to solve the problem was a very modest amount of exterior grading. Bholler's point about rain water not being groundwater is a distinction without much of a difference, assuming the water table is lower than your ash pits, fixing grading should prevent the problem. Your gutters may have been blocked by snow, letting the entire rain collection area of your roof overflow along the base of your walls. Moving the downspouts away only further suggests that grading is the problem.
TE
Rain water penetrating the structure below ground level is a much more likely cause. In my old house during severe thunderstorms, I could get a jet of pressurized water squirting into my basement through the water pipe penetration which was 4 or 5 feet below ground. All it took to solve the problem was a very modest amount of exterior grading. Bholler's point about rain water not being groundwater is a distinction without much of a difference, assuming the water table is lower than your ash pits, fixing grading should prevent the problem. Your gutters may have been blocked by snow, letting the entire rain collection area of your roof overflow along the base of your walls. Moving the downspouts away only further suggests that grading is the problem.
TE