I've cruised Quantum and Ovation 4 times out of Seattle in the past couple years. 10-10:30 is about when boarding begins. Look at your reservation. It'll tell you on what day your online check-in opens. To snag an early boarding time, you need to jump on it right away when it opens. I'm cruising Quantum again in a few weeks. I wasn't able to get online until the afternoon of the day mine opened and the earliest I could snag was 11.
I'm struggling to remember if JSs were included in priority check-in. Either way, I think the app SeaPass says "suite", so it can't hurt to try. π