While researching other possible trails near Mt Rainier, we came across the Eastern Loop. This isn’t an official trail, but a combination of a few trails to the east of the mountain that together form a loop. It includes the Wonderland, Owyhigh Lakes, Eastside, and Cowlitz Divide trails. At the north end of the loop, there is a short stretch of road (3/4 mile) that connects the Owyhigh Lakes trailhead to the Fryingpan Creek trailhead.
This loop is a bit longer than the Northern Loop, pushing 31 miles, and there are less camps along the way. Overall the elevation gain is less, but you do traverse the highest part of the Wonderland Trail as you cross the Panhandle Gap.
Eastern Loop elevation profile and map files are available here.