Big Pine, those round-trip hike times seem really ambitious, but you know your abilities.
And then traffic in SoCal can get really snarly, and that could put a big crimp in your time. Only maybe this year, with so many not working or working from home, maybe traffic isn't so bad.
To be honest, I'd give the hiking/running part no greater than a 50% chance of success, and the driving part around a 75% chance of success. So roughly 3 in 8 odds at best that I'd be able to pull off the whole thing. While it would be nice to be the first documented person to have done this, I wouldn't mind living vicariously through someone else's trip report(s) if someone beats me to it.
I'm also wondering whether a first-timer (I haven't done Langley before) would find it easier to do the 7-hour round trip from Horseshoe Meadows to Langley via New Army, or would have a better chance with the 3.5 hour round trip from the locked gate to White Mountain. You can't really get lost on White Mountain or have problems with route finding, but I don't know whether the same is true for a solo first-timer on Langley. Maybe I'd have to scout out the route beforehand.
That makes the Highest to Lowest I did with Bob Rockwell and his friends a few years ago seem pretty genteel. Rockwell planned it as a commemoration of Norman Clyde's trip 80 years before -- we started from the summit of Whitney (watched the sunrise after sleeping there), hiked down, and drove to Badwater. Took pictures, and then went back to Furnace Creek and had a great dinner in the restaurant.
If Death Valley and the hotels were open, it would seem possible to do the entire Lowest-Highest-Lowest trip between sunrise and sunset. There's no LA traffic to deal with, so the 135-mile drive from Badwater to the Portal can easily and safely be done in less than 3 hours. With 14 hours of daylight in late July, that leaves 8 hours for the round-trip Whitney hike. Still tough, but not insane.
It'll be breakfast at Furnace Creek, sunrise at Badwater, lunch at the top of Whitney, sunset at Badwater, and dinner at Furnace Creek. What a day!