Are both these stroke orders for 里 and 再 correct in mainland China?
I usually look up this dictionary for stroke orders. There could be some other useful sites like this one. 

I personally apply the second order for 再 and 里 as you quoted. In practice, the stroke order doesn't really matter and you can develop your own stylish based on the standard one. For native speakers, we would only be taught and tested the standard orders in primary school. It becomes meaningless when we grow up. We almost forget the standard orders for certain characters. When we teach our kids, sometimes we have to look up those authoritative resources online. 

I think the reason why we still need to learn the stroke order is that we need understand the conventions on how to write a Chinese character.