1st of all, I'm a pro safety engineer and i see EVERYTHING associated with ISSUES! Can't really blame me as it's my job to find potential issues with the probability larger than 1/1,000,000,000.

This is just to bring to your attention of potential issues:
Day 1, holiday traffic plus stops for food, rest area, and gas. If starting at 5am, more than likely you'll not hit Redwood National Park by sunset - sunset is real early now in winter time.
Day 2, same issue as day 1 plus coastal drive is slower and you have to obey speed limit as the consequence of off-road is real bad. And you easily add 2 hours if you stop for only 10 minutes for each state park. if you shoot sunrise around Redwood you'd likely miss sunset at Olympic around 1st Beach (it's a BIG park).
Day 3, assume you spend 0.5 day there in Olympic (attractions are not linked by road inside the park so you have to get out of the park then drive to the next attraction using the outer road - costs time), then your chance of getting to Mt Rainier before sunset is not good.
Day 4, assume you spend 0.5 day in Rainier (clockwise starting from the north) and at the end of your visit you're at least 1100miles and 18 hours none-stop driving from home (you need 3 gas stops)! You'll be late for work on Monday!
Safety: costal driving and Olymmpic/Rainier driving are far more dangerous than freeway driving and you can't set a time limit - it takes however long it takes to get there. Pushing the limit with an aggressive plan increases the risk...
Efficiency: overall ratio between shooting time and driving time is too small
Suggestion: book Day 2/3 hotels with the ones that you can cancel for free in a day or less, just in case, and be prepared to alter your travel plan according to your real-time progess.
Other option: LAX to SEA direct flight is about $400 inclusive for return tickets
Sorry to be the pest...