Snowpack Question – JMT Section Hiking

So after a solid month of trying, I finally got through the permitting process and have the official federal go-ahead to do a nice multi-day section of JMT, from Tuolomne to Red's Meadow. I'm hiking at altitude in the ANF to acclimate, I won't need to resupply, and my lovely wife will be doing the pick up and drop off (and living the high life at the Ahwanee while I'm hauling ass in the grass). The problem is that the date is fairly early in the season, departing June 14th. Given the section I'm hiking, and the Sierra snow situation as of today (30%), how problematic is snow likely to be? Will I need an ice axe, crampons, and a four-season tent? Or is it more likely I'll have a few sections of awkward snow cover that I can just push through? If the info above isn't enough, ask away, and I'll answer. Thanks in advance! WOOOO!