Hi,
Well, I roughly understood your intention, but let me tell you this. When you create GR/IR, it will adopt FM assignment from PO, including Budget Period. That is, if PO is posted in quarter 2 and assigned with relevant budget period, GR/IR even if posted in quarter 3, will have budget period 2. So, I don't see a problem here, if I follow correctly your requirements. Therefore, whenever you want to make Budget Period of quarter 3 open for posting, it will refer only to those stand-alone documents or new chains of PO.
Regards,
Eli