Aside from taking Bart, which is always the best plan from the east bay IMHO, you can get dropped off at the rental car center and take the air train into the terminals to avoid the nighttime terminal traffic. You could do the same to get to the Hyatt. I don't think you'd have much traffic issues getting off at San Bruno as if you're heading to the rental car center and taking McDonnell road south all the way to the Hyatt. The traffic jam is coming north on McDonnell Road, from Millbrae, where you're traveling the same route as seemingly every Uber driver in the Bay Area.

I hope they can fix the issue as it causes a backup in the Millbrae area and Old Bayshore Highway is jammed to past the Marriott as certain times of day. Maybe forcing Bart to charge normal fares to SFO instead of gouging with a surcharge will help.