PER-MEL-SYD is fine, you just can't* have MEL-PER-SYD

If you are simply looking to maximize distance you can do SIN-SYD-CNS-MEL.

There's not much more you can do with Europe, you have done well there.

There's no eligible west coast service YVR/SEA-SFO; AA codeshares on AS for these. Substitute MIA for YVR and you get this for 44890 base miles:

SFO-HKG-NRT-BKK-KIX-SIN-PER-MEL-SYD-LHR-IST-BUD-HEL-FCO-JFK-MIA-SFO

Here's a routing using FCO-ORD that visits your 'must do's' that earns 48,409 base miles:

SFO-HKG-NRT-DPS-NRT-SYD-CNS-MEL-LHR-IST-BUD-HEL-FCO-ORD-SEA-ORD-SFO

*(There are some exceptions but are not applicable to your routing)