So this may or may not help depending on the legendary run, so take this with a grain of salt. But for me I cleared the legendary run multiple times today at light 974. It was the quarry with unstoppable and barrier champions. The unstoppables with the flamers are annoying but will not heal so just keep throwing yourself at them until they die. The final room had the boss and spawned two barrier champions over the course of the fight. As you noted trying to drop their shield solo and survive the attacks is basically impossible at the moment. However you do not need to always kill them, I manuvered around to find places out of their line of fire to deal with the boss who while a bullet sponge is predicatble with his AI and you can generally avoid his attacks.
So it may not work everytime, or everyday but there are legendary lost sectors that can be done at the lower light levels if you have a high tolerance for frustration and don't mind smashing your head into a brick wall over and over.
Edit - Also if you unlock enough stuff in your bunker, the heavy frame absolutely melts them.
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Given the frustration, is it worth doing though?