Mansfield has lights on Gondolier, which is convenient since the top of the Gondola is the closest lift to Mansfield's true summit. On Saturdays through ~3/17 weekend it runs until 9:00PM. To do it right, you should also add Mad River Glen
Sounds like:
1) Skin Stratton VERY early, hike over to summit and back, ski down to waiting car before the lifts open.
2) Head to Killington (~60 miles, ~75 minutes) and up to summit/ski down (30 minutes?).
3) Off to Ellen/Abraham (~40 miles, ~55 minutes). Hit Ellen, ski down, cross on Slide Brook lift, do Abraham (120 minutes?).
4) Head to Mad River Glen (~6 miles, ~10 minutes). Up the NEW lift, summit, ski down (60 minutes?).
5) Off to Mansfield (~22 miles, ~35 minutes), up gondola, summit, grab a beer (gotta have beer!), ski down gondalier (120 minutes?).
6) Head to Jay (~43 miles, ~60 minutes), up Tram, summit, ski down (20 minutes?).
So, travel would be ~171 miles in ~4 hours. Lifts typically run from 8-4 on weekends, a bit later late in the season. I estimated VERY rough hike/ski times for all peaks and came out at ~6 hours. Even with a lot of luck, and a willing shuttle driver, it can't be done. HOWEVER - Mansfield lifts run late on Saturday... skin up Jay, ski down... Problem solved. Depending on how early you start, you could possibly get to Killington as the lifts open, which might then allow you to get to Jay ahead of Mansfield, and ride the lift (just thinking out loud). The biggest logistical challenge is skiing before/after dark. Might be a good idea to turn it into a charity fundraiser and notify the mountains in advance.
I'm starting to wonder why someone here hasn't tried this stunt: summit and ski all lift served VT's NEHH. Certainly a better man than I am!