GarlicJelly
Friendly Moderator (Formerly known as GoodStuff)
Own pointed out in the Speedrunning thread that you don't actually need to phase over and activate the computer after beating Phaseman.. Just posting it here to make sure it isn't overlooked, just in case it's something that you'd want to fix. 
From now on you should immediately teleport back to the start of the Flying Fortress as soon as you get Phaseman's power. Don't warp over or activate the second computer, it's not necessary. Only computers 1 and 3 need to be active to proceed.
Though, you can go 1 -> 3 -> 2 if you want to see a light ding in the middle of the blackness. It does nothing.