On your operating system you can setup different printers with different printer trays as default.
Firstly, I agree your view, that's maybe a workaround.
But it still can not resolve this issue.
The background is:
This is a print batch job, can not setup the printer properties manually.
All documents are proposed to be printed on a printer because of the sorting issue, so we can not setup different tray for multiple printers.
I researched 3 days for this issue.
Till now, the only solution i could try is:
Setup the specific tray by WIN32API, then use acrobat to print, after printed, roll back the tray set up again. However it will cause a performance issue.