They shouldn't make one of the regular episodes public due to the risk of pissing people off and "breaking" their promise. Lots of people are fickle. In my opinion the best sort of "teaser" for the Cup of Jones episodes that still keeps everyone happy would be to make one bonus episode a month that's a bit wider reaching and calling it something like The Monthly Goblet and in that make sure to pimp the weekly show, so people get continuously reminded of what they're missing out on without any actual episodes being made public.
That shouldn't be too much additional work for Brandon, it's one video a month, and it would give extra content to the Patreon people so they'd be happy, it would give a little taste to the regular viewers so they would be happy plus it would potentially convince some of them to sign up for a dollar or more if they were hesitant about the quality of the content behind the paywall.