You better check if this is wise. Late snowmelt this year means, most of the trailheads to the summits are still under snow. Fast climbs are not going to be achieveable at this time of year.
This is my GPS track for when I climbed Mt Jefferson on July 28, 2010. The violet cameras are where I took a picture, looking up/or down the mountain. Numbers are the time I took the pictures. There was still snow on ground in Shale Lake area as that date.
I can send you that GPS track, but I don't think it's the one you want.
Here is view from Shale Lake and the valley ahead. Expect more snow on mountain and completely around the lake in forground.
I climbed the wrong side of the valley above Shale lake... and would recommend the east side. But if you encounter plenty of snow - just climb straight up the middle of the creek.
Once the top of the "V" in the valley is reached... it's a piece of cake to reach the Red Saddle.
The terrible transverse and the final 200 ft of climb is yours to plan. I never tried it.