You could look around for a used Benateau Class 8. While technically it has a swing keel, that keel weighs 1100 lbs so the weight is down where you want it. Its on a hand crank threaded rod, so it stays in place. It has an open transom and tiller steering. You can trailer sail it, but stepping the mast is a pain, as it is a keel stepped mast. They sell pretty cheap used, so well within your budget.
It is a racing boat, so it should sail well.
It is a racing boat, so it should sail well.