If you're physically conditioned enough to do the traditional trail without being dead on your feet, you should be OK on the MR. Depending on the season, it would be important to have some snow/ice experience with crampons or micro spikes and an ice axe/trekking poles. We brought the former in both cases but only had to use the latter (spikes/poles). If you plan to glissade, be sure to have an axe.
The E-Ledges are scary for some folks, but we found them to be fun. If one is that scared of heights, maybe a different hobby should be under consideration?
As the other person said, it is the same altitude gain over 7-ish miles vs. 11 miles, so the MR is more steep.
If, by "heights," you mean precarious heights, we had no issues. The slog up the chute from Iceberg Lake is physically demanding. We had wet snow and had good traction with spikes and noted that it would be a bitch without snow.
The key factor will be what happens when you get to the notch just below the summit. With no snow, the "Easy Walk-Off" route is simpler, but is treacherous with snow/ice. We opted for the climb... and did it without ropes. Again, there was no snow or ice on the climb so ropes weren't necessary.
If you're wigged out by some easy-ish climbing at 14,000 feet, either bring ropes and gear or hope for no snow and take the walk-off for the last bit. We LOVED the climb to the summit. I also loved the fact that the MR is shorter.
I studied lots of websites, and printed out a nice route description and brought it along. It came in handy - because the trail isn't as defined as the traditional route. Some say the MR isn't a proper trail and I'd concur to a point. If you're good with route-finding, you'll be fine. Remember to walk on rocks and not trample the plants.
As for acclimatization... we hiked up to Lower Boy Scout Lake the day before because we nabbed a pair of day-of walk-in passes. You could just as easily hike up to Lone Pine Lake and spend some time there. We slept in Lone Pine the night before the hike and drove home to Los Angeles after the hike on Sunday night. Truth be told, that was the hardest part of the entire day for me.
As for beer - I didn't bother keeping it cold. I brought a nice beer that would taste fine at the ambient temperature on the Whitney Summit - this time, a La Cumbre Elevation IPA. It was damn fine.
