First: You have to think positive about it. Once she has it, pretty much no one (sans a court) can take it away. So, it's worth the time (even though it might not seem like it now). Deal with each little problem as it comes.
Now, I have two questions that might or might not help steer your direction:
(1) Can she apply to the Uni before the process is complete? They surely won't be sending out acceptance letters before June/July. That said, must she prove status in her Uni app? I know when I went to school, they only asked for proof when it came to signing my student loan. She can probably get the process started. It does carry the risk, that, if she doesn't complete the PR before start of school, she'd be on the hook for the international student rate (yeah, I know it's a big risk -- but calculated -- like poker
). This is something you might want to run by the intake personnel at the Uni's enrollment office.
(2) Have you considered applying for a student wisa? As a stop-gap, so she can still apply now, and commute her status later?