There's another pre-gluing stretching technique:

get the tire across your body, looped from your shoulder down to your waist.

kneel on a clean floor and bend down to be able to loop the tire under your shins.

gently try to straighten your body so you feel the tire pull at your back

I tend to increase force really gently until I feel just a bit of elasticity, then try to get the tire on the rim.

I worry that it's possible to overstretch the tire and break a few carcass threads. I think these would be fatal flaws.

What I think is good about this is that the added tension is the same all around the tire.