How to get threads in a yeast dough?
Damn, that looks good. I've never made this particular type of bread before, but here are some things that I do know which might help:

Butter is (roughly) 10% water and 90% fat, while lard is 100% fat. So if you substitute one for the other, you should adjust the amount of water in the recipe accordingly. The flavor will be a little different, but I bet either one would work.

I would not assume AP flour. In fact, I'd assume high-gluten bread flour. The gluten is what creates those fibers. It's the fat that keeps it tender.

This looks very similar to a brioche, so you might want to look at brioche recipes to learn some of the principles. One thing that most of them will tell you is to to knead the dough to develop the gluten fibers, and then add the butter. This I think is the key. I know that fat can keep gluten molecules from sticking together into strands, so if you add the fat later, you should wind up with strands of gluten surrounded by fat.