There are all kinds of routes, if you put no limit on length/duration.
You could go down the Mist Trail, across Yo Valley, up Snow Creek, cross the road, continue to Ten Lakes, and travel onward to May. You could go up through Cathedral, cross the road, head through Tuolumne Meadows out to Glen Aulin, and head up the trail from there.
I didn't expect that, since the majority of hikers don't do that kind of miles in a single day - you've already found the shortest route and it's pretty long....
So no, that's about it for the good routes. If you have a wilderness permit be aware that they consider walking along roads as exiting the wilderness. Crossing them to continue on trail is okay.