(Okay -- so the original post on downtime was OOC 119, if others are looking for it.)
That post talks about an old UA, which in the end, I kind of threw out (not on purpose) and just went with a much simpler (though perhaps more confusing, if you're not used to it): "Tell me what you're doing. Roll three skill checks that you think might be appropriate. I will tell you how it works out." It's what I did back then, and it's what I mean to do here.
You don't really need to "choose a downtime activity" (though feel free to check their list for ideas, if you're stuck), just think of what your character wants to do for a month (though the character might not know it's going to be a month, they may have moved on with their lives and will get dragged back into adventuring.)
That kind of thing is up to you, as long as we find an excuse to keep them in the game.
For example, Dandin probably assumed that he could avoid any more life-or-death adventures, and is simply building his shipping empire. If he decides to risk the trip to Waterdeep, He'll probably want to roll something like:
Persuasion (to gather a good crew);
Survival (to make good choices at sea); and probably
Persuasion again (to do some serious trading in Waterdeep
I'm not sure how much of a sailor Dandin is. The survival could be Int (Navigation) if he has the tool proficiency (or even if he doesn't) or Vehicle (Sea), but he could leave all of that stuff to Janus and roll more leadership-type stuff. He's got professionals for all that, after all.
Though in this case, because it's so interesting and important, I think I might roll all of that for Janus, or get 'Goyle to do it... I'll think about it.