The earliest I've checked into the HR SFO is noon. If you contact them ahead of time they are usually pretty good about getting people into rooms early if they can. Going into town with BART involves taking the HR shuttle back to the airport or take the SAMTrans bus (stop across the street), uber, or walk to the Millbrae Bart Station which is two miles away. The HR shuttle to the airport is easy as the shuttle goes directly from the HR to SFO.

The HR SFO shuttle from the airport to the HR stops at the International Terminal and the Marriott before arriving at the HR. I've been pleased with the shuttle the last year and haven't experienced any of the delays that regularly used to occur. There is a display in the lobby (and an app) that shows the location of the shuttles. Breakfast at the HR is better than the breakfast at the GH SFO.

The GH SFO is usually much more expensive but the convenience can't be beat but that convenience is not usually worth $150+ to me. The GH SFO used to have an early check in fee where you could sort of guarantee an early check in. You could contact them and see what they say.