For Eel Bay, you enter the park and take the first left after the gate (toward the Minna Anthony Common Nature Center). After about 1/4 of a mile you'll see a small boat launch on the right & plenty of cars parked with people fishing Eel Bay. Most areas are productive - out and to the right a little works well.
And you are correct if you go to the main boat launch at the marina in the the State park, that's a different part of the river (though it is fished less over there and I've caught the odd fish from time to time).
You can fish right in Clayton if you want but you'll probably get more consistent action in Eel Bay. In Clayton - you can access French Creek Bay from the public boat launch next to the Antique Boat Museum.
Good luck in the tournament!