In mid-June, there will still be a lot of snow, and I would just plan on using crampons. The "chute" (slope west of the 99 switchbacks) will be the route everyone is using, and crampons and ice axe are what you need for that.
Since there will be so much snow to cover, you will need a super early start to day hike it.
As for joining another group, most people don't invite people from on a forum. But you will be joining many others doing the same thing, so you will not be alone.
