I would consider an alternative periodic table a success if it predicts new elements or new interactions that the old one didn't.
This, right here. This is the only valid argument for changing an existing and well-understood model when there's no new evidence to consider.
The Periodic Table isn't a model, or at least not a functional model. It's a chart - a way to represent data. Arguably, a chart is a model of sorts but considering your comment concerning "new evidence," you certainly seem to be implying that it's a model of how things function and this new proposal provides an alternate functional model, which isn't the case. The proposed alternative isn't a new theory of elements. It doesn't change our idea of how things works. It simply presents the same information and understanding in a different way. If the new table doesn't provide any new predictive ability at all but it does, say, present the information in a way that's easier to grasp or makes relationships clearer, then it's worth considering and possibly worth adapting.