Hmm, considering that we want to get as many people as possible over the course of time, I'd say we let it alternate? One week Monday, one week Tuesday, one week Wednesday.. We'd have to strongly rely on the rest of the community for this, but by now there should be a big enough experienced playerbase to draw from.
If people see the Battle the Invincible Art Team pop up at their Steam account, they'd surely see the "New Player Training Game" as well. With some luck, not only new ones would respond to that call, but also veterans that'd be willing to aid a hand, even if they don't step up here on the forum.
If it's a single day every week, I'd fear we'd let many people slip trough that net.