Good to know I've helped you Adam
Essentially it's a trust & bonding exersise, the more you sit there with him & do it, the more he will learn to trust you. Flocks of budgies will do this to eachother if you watch them, or pairs with eachother.
Another thing that may be of use to you, is if he screams or sqwawks at you, try whispering to him & trying a 3-step warning system to a Time Out.
A firm but quiet No, praise if he stops, then repeat twice more if he doesnt, then silently put a black sheet or such over the cage & tell him "Time-out!" and leave him for 10-15 minutes. He should remain silent, and if he does, remove the sheet while praising him & use the word "Quiet" alot when he is silent, it comes in handy later if he begins to associate it.
This way, you are not encouraging him to scream by screaming back at him, and punishing him with a breakoff from his "flock" (you), and by him being quiet, he gets rewarded with the return of you, which is what he was screaming for in the first place. By bypassing the attention-screams and teaching him this system, he will learn not to screech for attention.
Eddie doesnt utter a word unless he's singing to some music or he's replying to a bird outside. Living in a flat, a quiet bird was essential for me
Hope you find out whats causing your wee budgie's sneeze-a-roozles .