Yes when I was a kid I did the [Censored] smith kits with soldering and it was bloody hard. I used to always get mums friend to finish it for me.
That's a funny story about your foot on the soldering iron. Although not funny for you, a bit of a Homer Simpson moment.
Just an update on the job.
I pretty much followed your advice and it came out well and it's really comfortable for pulling down the door especially with two hands. I couldn't get a metal grommet and even if I could I don't see how I could have crimped it in the hole. I just used the rubber one so thats probably the weak one so let's see how long it lasts. I used the 3mm plastic coated cable. I used the 5mm cable tie backs you referenced in the 3mm. Then a clear pvc pipe and the insulation tubing you mentioned.
The insulation you mentioned does make it nice and thick and soft.
Photos below
I also changed the locking spindle and it opens and closes fairly easily.