Ok, we have the official snowpack for this year, and it is less than last, barring a very unusual late season monster storm.
The Tuolumne Meadows rangers report 20 in of snow has melted there in the last ten days. They have 39 inches on the ground.
Last year, the road was opened may 21, and the current year seems to be a week or two ahead of last.
All things equal, you should be in good shape.