Think your route looks good. I would not miss Rainer or St. Helens, and would camp at Randle for a full hookup or near by boondocking. Then it's south on rd25 to the east side and a great view of the St Helens up close and personal. But if you don't get enough you will need to head towards I-5 for the visitors center later in the trip for the full meal deal. Next to Elbe and the Nisqually Entrance to Mt. Rainer, this gets you some of the best views of the Mt and all the hiking you need. You can see the number of days needed nut this will give a good taste of both mountains.
Next I would head to Aberdeen west bound to I 5 and SR 12 to Elma then SR 101 and on to the Hoh rain forest( Good camp ground at the visitors center and lots of hiking). If you can work it in before the rain forest and get reservations Kalaloch camp ground for 1 night and views of the ocean. There are so many places to see like a drive out to the most NW point of the US Neah Bay(views are sooooo good and there hiking there also. There is Solduc Hot springs next but I would not overnight. On to Port Angeles several CG's here with great access to Hurricane ridge and lots of views and hiking trails. Also take the road to Obstruction Point Trailhead, good hiking here to. Then on to Potlach State park for a taste of Hoods Canal. Now your almost back to I-5 and you can if time allows hit the west entrance to St. Helens, then to I 84 and Pendleton. On this route there are many pull offs even in tow to see small hike side routes. No worry about fuel and other services along the route. Have fun!
LEN