I had a similar problem with my boat as well. On my BT166, there is a drain hole around the rim of the door. There is normally a tube that is hooked up to this drain hole inside the compartment area, but My tube had broke-off. Once I replaced or repaired this and hooked it back up, the problem was solved. I haven’t had any issues.
I also turned one of the Livewells into Dry storage by plugging the drain holes and taping off the overflow tubes.
As for the regular storage bins, I would check out the drain tubes to see if they are plugged or broken. Not sure what to say about your rod lockers. I haven’t had an issue with them.