Hi Nick,
My hiking partner and I did Forrester Pass in the first week of July last year. The majority of the snow started about 12500 feet. There was definitely a good amount of snow, but not quite enough to need crampons. This year is different, however; the Sierras have much more snow this season than last. Sequoia is listing their snow line at 7000 feet right now, and although it's melting pretty quickly, there will be a good amount left at the end of this month.
I would probably recommend crampons over the microspikes, unless you are planning on hiking Forrester very early in the morning before it has a chance to soften up. Parts of Forrester are fairly steep, depending where the boot pack trail is located. Oh, and watch out for the mosquitos in Vidette Meadows!
Have an awesome trip and hike safe!
Katie