RKS,
The MR itself in general is visually straightforward as seen from Whitney Portal Road. The information contained here and at summitpost.com has plenty of good information to peruse. In addition, from a climb this past winter, I put together a video that describes the MR all the way to the top (
www.customflix.com/205683). Although shot during winter, the main route segments are the same.
About snow conditions, based upon recent reports, there's still plenty of snow up there causing plenty of people to turn back even on the main Whitney Trail. I was in the Eastern Sierras over Memorial Day weekend and was surprised to see so much snow in the entire Sierra range. Keep reading the messages since the good people on this message board are very conscientious on posting up to date conditions which are very helpful.
Are you saying that you did the 11-mile Whitney trail to the summit in 4 hours? You might check your numbers, but assuming you are right, that's incredible. Although the 4.7-mile MR is shorter, you do ascend more quickly putting different demands on your body than the mail Whitney Trail. Spending a week in Yosemite's high country will definitely help in conditioning yourselves.
About permits, I only have been in the Whitney area during winter months so I'm not an expert on the permit requirements during the rest of the year. (I'm one of those winter junkies.) If you don't get the answers you need, call the Ranger Station or the Whitney Portal Store. Even if you don't need a permit for a one-day MR climb, it would be a nicer experience overall not have to "rush" to the peak and back, especially for safety's sake. You'll want to be careful in the Chute, the most exposed part of the MR, above the Notch. I understand the MR is pretty busy this summer.
Hope some of this helps. Good luck and have a great and a super safe hike/climb in the Sierras!
gosc