I hope you watched the videos too then cause I show how I did it. Basically the technique is the same for touching, grabbing, etc. You put your hands as close to the parrot without it freaking out, wait, withdraw, reward. Progressively get closer and closer till you can touch its wing with a finger, then work to cup your hand around the back, then to briefly lift, etc. Basically you just do more and more but without going so far that the parrot doesn't get too freaked out. You hold the duration progressively longer as well. First 1 second touch, next time 2, etc. The concept is exactly the same whether you are doing finger touch or putting on harness. You are just progressively increasing the duration and rewarding the parrot tolerating it.
Check out the one person bird article. While it talks about having a second person taming your parrot, the techniques are mostly the same if the first person hasn't already done this to begin with. Basically Kili had to be re-tamed by another person so the original taming techniques were repeated. You can ignore the stuff that is about other people but follow the steps the second person should take yourself.