Best guess, expect mostly muddy trail below 10,000' and snow, ice and mud from 10,000' to 11,000' followed by mostly ice and snow with scattered mud to treeline. Then patches of snow to climb over in the areas the winter drifts were large before the trail dries out and is clear above the saddle. I have my next hike scheduled for the 18th or so and am hoping it will have improved a good deal by that time. The best close spot for a campsite is off of Freidlein Prairie Road about 1 1/2 miles up Snow Bowl Road. It is a busy area so the FS installed numbered sites on the road, but they are free. Elevation is around 8000'.
I think Monsoon season will begin around June 20, plus or minus 5 days, not by the calendar according to the NWS, but when dew points rise dramatically, and it begins to rain over the Sacramento Mountains. It will start about 10 days later in Arizona.