Nic, if you and your GF can do Shasta, then you will be ok on the MR. If you can do Shasta in two days, I think you will be fine on the MR in one.
June will be a good time to do it, as you have more daylight. Starting up the Main Trail in the dawn twilight should be as early as you need. The Ebersbacher Ledges are best done with daylight. Make SURE you study the route. Have you seen the
MR Info on this site?
I doubt road construction will be up on the Portal section that early (but I could be wrong). Transportation will be a hassle if you can't drive up and park.
Don't take rope and harnesses. Guides do but others don't. You will want to decide on the "Easy Walk-Off" vs the "Final 400" once you get to the notch. In early June the F400 will have some icy sections, or it may be steep packed snow that work well with crampons. The first part of the EWO would be the worst for ice.
The "trail" is just a use trail, and is not so well marked. You really do need to study the route so you know where to make the sharp turns. Knowing where to go will save you lots of time and frustration.
As for permits: The Lottery is for Whitney Zone Day-Use, and overnight on the Main Trail. If you day hike the MR, you need the WZ Day-Use. (But there are so many no-shows in early June that walk-ins will be available the day before) To overnight on the MR (I would recommend Upper Boy Scout Lk), you need the
North Fork of Lone Pine Creek JM34 permit: quota 10 per day, 6 reservable through that link, 4 available at 11 AM the day before to walk-ins.
