There aren’t really that many options for ‘quiet and secluded’ unless you want to chance camping in the river bed, which is not technically illegal but can be dangerous.
JFK Park has very nice facilities but they are crowded and popular with the motor home set. Lobo Landing has a private camping area but I don’t recall there being any public facilities. You might have the option of camping on the lake side and getting away from the crowds but you would not be on the river itself. I’m not aware of any camping options in the peninsula area tipped by Cow Shoals, but there could again be some kind of private site I am not familiar with.
Good luck!
Zach