Let me clarify....So you are flying SEA-SFO-SYD, and you want to check a suitcase all the way through to SYD but "short check" the painting SEA-SFO only?

You definitely can't have the painting tagged all the way to SYD because you will not see SYD-tagged luggage at SFO. You need to ask the agent at SEA to short check the painting for you... I have done this before and had no problems. I suspect you will be OK especially if you explain why you're doing it..and if you have a comfortable enough layover at SFO to give you time to go to baggage claim and pick up the painting.