How thin is “very thin” for the day old croissant slices?

Your question about width of slices makes me think of the trouble you might have with slices from any croissant unravelling.
To make this recipe work better, I would use rolls that have been allowed to go stale several days (not just one) or frozen. Either of these two conditions will hold together better when sliced.

I'm not sure if I would have any high quality croissants left the next day to make these. And for sure, I'd rather expend something reasonably priced the first time around. After all, you are repurposing something stale that is no longer in tip top shape.

I've never had a Costco croissant so I can't comment specifically on that.

I would likely try slicing the croissant between 8-10 mm thick depending on its consistency. It is probably easier getting thinner slices from a more mediocre, breadier croissant than a premium, flaky one.