One note, based on my experience in across a variety of organizations, including holding a leadership role in a small political party, is that when a debate is "Free Flowing", if it is taking place verbally (usually in-person or over video-call) the lack of definite structure and time-boxing can often lead to domination by whoever of the two or more interlocutors has either greater prowess in rhetorical skill, or is more willing to simply steamroll over the opportunity for the other to speak, or both. I think a balance may be struck by having structured rounds, with a pre-established limit for the number of claims each side may argue for or against, and then also allowing the debate to last some arbitrarily large number of rounds.
Much of the rest sounds desirable, though (as is also true of "Fact Checkers") difficult to accomplish in a way which will satisfy all parties involved. Choosing someone or some group with a genuine openness to whatever the truth may be (or as close to that ideal as any person can have) is the most impactful action.
Does anyone here know of good examples of such forums for debate, either (recent) past or present?
As a parent of young children, I often consider this very dilemma. In addition, as the other comments describe, there are several other dimensions along which a parent must optimize:
This is a place where I find traditional wisdom to be useful, since the constraints and values faced by parents have been largely the same since the invention of writing. (At least, for those who could write.) Consulting a variety of such works, both those which address the topic of parenting directly, as well as those which do so obliquely (typically narrative fiction of particular importance or cautionary tales), one can form generally-useful views, even if none seem universally-and-definitely useful.
Though I admit to thinking about this in this level of detail only as a result of your post, the main such points, 18 of them, in my view, are perhaps the following: