Nice pictures of your outing, that's old school. Early black Coleman, Kampkook, PW or this 1914 Gates Folding made in Newport KY. would work.
A lot of our campgrounds specify gas cooking. I chose white gas. In reality the rule is meant to mean no fires so any safe fuel cooker would not be disallowed
Much of my cooking is over an open fire but as you said campgrounds frown on more traditional cooking. Also being a more modern era I can reduce weight using a stove instead of cast iron.