As an Adagio main I have to disagree with most of your Support section. In the current meta a Captain should really do about 1 rotation through the jungle and spend most of the time in the lane. Why would you rarely use your B? You have a way to make your teammates stronger, why wouldn't you? Echo is almost completely useless on Adagio, especially as a support, because his ult isn't going to do any damage if it's successful when you're built as a support, and as Radiance pointed out, you don't need a battery. His heroic perk keeps his energy full. Not to mention so many support items Like contraption and stormcrown have energy or energy regen. These are just my opinions, but I appauld you for going outside of the box with your builds.

Good sir, why do you use so much Echo? O_O
Verse of Judgement is very easy to block the first time, and the second time, you will not have your stun due to you popping your Gift of Fire for the first stun.
And Adagio's Arcane Renewal makes Void Battery pretty redundant x.x

Great guide! :) The threats all make sense, well except maybe Lyra. I am a Lyra main and against a Lane Adagio, I often have no problem in a 1v1. Her damage output is much higher(with Shatterglass and Alternating Current, sometimes broken Myth) and in any case that she get's out matched, she can do her bulwark and and teleport away. Can't she compete? I guess it is just your experience. You might want to put her a little higher up. But great guide! I would like to try your build as I just got Adagio from a Mystery Chest! :)