The west coast is a big place. Two factors will come into play here.
First, are you thinking about Seattle or San Diego? Your route would likely be VERY different for those two destinations.
Second, the weather. Leaving now and heading for Seattle along a northern route would entail some risk. If you are not as you say in a hurry, you can do that. Not my favorite as we like warmer weather and so does your coach. Not all campgrounds are open either so that adds some cerebral activity.
Maybe some more help with your "goal posts" would get you some specific answers that you can use.
About the car, been discussed many time here and elsewhere, but your size rig means you could leave the car at home. Not many places you can't access with a 28 foot rig including practically all sites you want to see. Parking in a big city can be tougher, but that would not be a problem very often.
I have often wished we could get by without a car as it gets to be annoying hooking and unhooking, not hard, just another step in the process that is sometimes done in the rain. We are 40 feet so NOT doable without a car. Yes, you can rent, but we like to be out and about most days so rental cost would be way too high. We spend one day in ten at the park without leaving. You may be different so do the math.