Considering he nearly rode 50km solo and only finished 1m25s behind Vingegaard who got dropped off 10k from the top, i would argue he did a better job, relatively speaking.
TT bike all the way seems like the worst idea. I don't think you'll get much aero advantage on the climb at those speeds (~22kmh) while TT bikes weigh considerably more. In an ideal world, a bikechange would probably give the best result, start on TT, change bikes, road bike on the climb. I think you could win enough time on the TT bike on the flat to warrant a bikechange. Assuming the bikechange goes smoothly. A road bike with aerobars is also an option.
TT to roadbike change > roadbike + aerobars > road bike >> TT bike
Say you can do 59kmh on flat sections on a TT bike, and you could do the same sections 54kmh on a road bike, you would take 213 seconds on a TT bike the first 3.5km and 233 seconds on a road bike. So a 20 second difference, meaning a smooth bikechange could gain you a few seconds. But if something goes wrong, you would easily lose that time during the change.