Peggy Goldman has updated her book, "Washington Scrambles", published by the Mountaineers and available in both print and e-book (PDF) formats. The book has 8 scrambles in Mt. Rainier NP, most of them in the northeast quadrant of the NP.
The book has an 18-page introduction and overview of the scrambles, all of which are non-technical hikes and scrambles, but some hiking and scramble experience is preferred. The chapter has advise for the various possible conditions for the hiker, weather and other factors.
The book has an overview of the presentation of the areas and scrambles in the book. The scrambles for Mt. Rainier NP are:
Echo Rock and Observation Rock - Northwest
Mount Ruth - Northeast
Goat Island Mountain - Northeast
Banshee Peak - Northeast
Governors Ridge and Barrier Peak - Northeast
The Palisades and Marcus Peak - Northeast
Tatoosh Traverse - Southeast
Mount Wow - Southwest
The book has excellent descriptions of the trail and scramble with map with each scramble. The book covers the whole state where only about 20 pages are devoted to scrambles in Mt. Rainier NP which makes the e-book nice if all you want is a specific area than the whole state.