Since it looks like you can not have it all, here are 2 options,
Dana (pacific seacraft) 24, built like a tank, shallow draft, slow but the weight, near full keel and inboard power might end up being a great option in your chop.
Re-consider the Cat 27, the benefit is they are cheep, have inboard power, and are easy to fix with lots of parts and advice available all over. You will break stuff, but will be able to get back out for less $ than most other options. You said it is too cruisy, but with 20 kts of wind every boat you will look it will be way overpowered anyway.