When the gates are open and the road is clear, fining a parking spot at the Portal (near the trailhead) is not a problem. I usually sleep at the Portal before heading up. That being said, you have a few other things to consider for MR, including route finding and snow conditions (even with low avalanche danger traveling on slushy slow can be a nightmare). I'd be particularly concerned about navigating E-ledges in the dark, both on the way up due to early start and and on the way down due to unexpected delays.
Edit to add: I left my reply unfinished to walk the dogs and didn't see John's post until after I got back and posted mine. His advice on scouting the ledges area a day before is very good. Also, make notes on how key landmarks look in the opposite direction in case you need to descend in the dark. On my first Whitney trip in 2008 (East Buttress c2c), my partner and I approached the route with two other climbers with good knowledge of the area who then parted with us to climb Mt. Russell. We followed them on E-ledges before sunrise and then struggled to find the correct path on the way back after sunset.
Last edited by Anton; 06/21/20 09:35 PM.