Try taping paper towels along the waterline inside the locker behind the rudder post. I assume that you have already climbed in via the access hatch behind the headboard. The hull is joined to the deck very close to the waterline at the stern. It can split in this area and allow water to enter. Wide masking tape will hold the paper in place at the hull is smooth above the join. It is easy to check if there's a split near the centreline, just reverse pretty quickly for a short distance. You should see water well above the join if you look over the stern whilst reversing at reasonable speed. Keep the helm amidships when going astern, it will obviously want to whip hard over and could cause some damage if you let it go suddenly.
Checking for a leak further up is trickier as you will need to sail well heeled on either tack in quite strong wind. Stick paper towels well up each side in case the leak is high up. A leak well off the centreline would leave the middle towels quite dry as the water won't run uphill when heeled.
The top of the rudder post is another possibility and it's worth taping paper towels on the flat area below the quadrant.
I think that these steps will allow you to track down the problem if it relates to the rudder or hull joint.
An exhaust hose is another possibility but that would appear when motoring in any weather. I discovered that my hose rubbed against sharp edges in 2 places inside the stbd aft locker. I had one tiny hole and a stream of water collecting below the drive shaft. Easy to fix by chamfering the woodwork, reinforcing with vulcanised tractor tyre patches, sleeving with plastic pipe and putting 2 jubilee clips over that in area where it wears. It doubt your problem relates to the exhaust as you mention heavy weather and not motoring.