I gave this challenge a go last night. I'd taken a total of 4 damage by the time I got to the chained court, but didn't have berserker, and I think I killed 1 opponent in the chained court before I died.
My usual tactic for CC+ is occupying one of the leftmost doors from the bunker, corner shooting until a baron wanders in from the right. I then leave the starting bunker to the left, and walk around the top of the bunker. The top area, above the bunker, is my favourite part of the level for line shooting barons, and I hang around there as long as possible, sometimes doing another 'lap' in running mode through the starting room or around the bottom of the bunker.
On AoH, though, even with hellrunner, there's basically no chance of taking it slow like that. I'm starting to wonder whether I should immediately use a berserk to get up there, and use the other berserks every time I do a 'lap'... I'll have another try tonight.
ps. I think doing UV AoHu as a conquerer without taking berserker might actually be reaching a bit far for me, but I'm enjoying exploring the idea. I think you're on the right track, though, with your build.