Coastal monsoon is honestly the final boss for cookies, this one defeats plenty of professionals too.
Biggest fix first: bake a couple of minutes further than feels right. Most "soft by day 2" cookies were carrying extra moisture out of the oven itself, and it migrates to the surface later. And cool them completely before jarring - pack them even slightly warm and they steam themselves soft from inside.
Then pack small. A big jar you open 20 times swaps in wet air 20 times. Small pouches opened once each, heat sealed if you can, with a 1g food-grade silica sachet inside (cheap in bulk online). That combination survives Kochi.
And teach your customers the rescue: 4-5 min in a 150-160°C oven, cool uncovered, the snap comes right back. A soft cookie isn't spoiled, it just absorbed water.
There's also calcium propionate (0.1-0.3% of flour weight) if you courier at scale, but for a fast-moving home bakery I wouldn't touch preservatives yet. Tell me how the drier bake goes?