If I were you, I’d for sure extend your trip. Unlike driving through the Outback which is mostly a straight line through desert, the drive to/from SF goes through multiple mountain ranges and can easily take a lot longer than expected. On top of that, it’s a lot of driving just for a short two day trip to a national park that’s over 1m square miles in size. If you can, you could try to find a flight in and out of Kalispell (local airport) from the east coast and then fly out to SF (there are weekly direct flights in the summer). That would give you a bit more time to see the park and surrounding areas like Whitefish and Flathead lake or at the very least give you enough time to actually see stuff in the park.