Is it possible to hold two Chinese visas in two separate US passports at the same time?

So, here's a complicated question:

My wife and I are moving to China on Z types to teach English on in mid-August. The ones we got are single-entry, and we'll need to apply for residents permits once we arrive. However, my wife needs to go back to the US for a week in September, well before the residents permits would be done processing. Currently, there really isn't a good way to do this, but I'm wondering if this would work:

My wife applies for a SECOND passport from the US government. Assuming they issue her one, she would then apply for an L type with this second passport. Assuming THIS is granted, she would then have one US passport with a Z type (Passport A) and one US passport with an L type(Passport B). She would use Passport B with the L type to get into China in mid-August, then depart for the US in September. After that, she would fly back to China a week later and re-enter on Passport A, with her Z type. Then she would begin the process of applying for her resident permit.

It sounds good in theory, but would this even work? I know it is possible to get two US passports, but is it possible to hold two Chinese entry permits at the same time (provided they are in different passports)? Or would applying for the L type invalidate her Z type, even though she would be applying with a secondary passport?

It's a pretty tricky situation, and I haven't been able to find any information about it online. Likewise, I have called several services and no one seems to be able to give me a good answer. Do any of you have any thoughts?

Thanks!