I wasn't too far off. The SJ train was 20 minutes behind schedule.

We walked all the way over to the T5 check-in desks, approached one of the three severely bored TAs, and we were checked-in very quickly. We were able to sleep in longer than usual at the hotel, take the shuttle, and proceed directly to security with plenty of time to spare.

This will be our SOP from now on. So very convenient. Although, finding a better hotel than the Park Inn would be nice.