So OP would just board the plane with an expired GC and I-90 receipt (assuming thats what his/her airline will require) and once they get to the border they can either:
A) file I-407 if they are happy to relinquish their LPR status and gain entry by paying/completing I-193 as they would likely have their visas waived being an AU resident
B) choose not to file I-407 and go through the process of attending court etc
Asking because I have a family member who is in a similar situation. Thanks.