So, I figured I'd try Shield Charging Megalesios, before he got his barrier up:
(https://s14.postimg.cc/49fp6rkj5/2018-04-30_1019_1.png)
(https://s14.postimg.cc/5bpvpby7l/2018-04-30_1022_1.png)
He ends up not being able to break the Conduit, but also being immortal. You have to Portal out, or stand in front of his beam to let yourself get killed, in order to proceed. I opted for the latter, as I didn't fancy running the whole maze again. Of course, then I had to fight both him and the Statues at the same time, which was a walk in the park for this build though.