To get the fibers from yucca I cut a leaf off near the base, then I use the back of a knife to scrape away all the green juicy stuff-- both sides-- until only fibers are left. Some people use a spoon.

The yucca I have here have very thin leaves, but they are a couple of feet long, so I can get a foot or so total of cordage from each leaf I put into the cord, unless I need it to be thicker. This stuff is STRONG. I got someone to tug-of-war with me to try to break a yucca cord, but we couldn't.

Here's a small cord I made a couple of days ago from one yucca leaf:

This is 11.5" long (I just now measured it) not counting the knot. It took me maybe 20 minutes to make.

The cord I have in my bow/drill set is a little thicker and a bit over 3' long. It took maybe an hour and a half to make, including preparing the yucca. Splicing the fibers together slows things down a bit.

The easiest cordage I've ever made from yucca was from leaves which got pre-stripped by the lawn mower. I just cut them free from the plant, wet them a bit, and twisted them into cordage. That is also where I got the fibers for my first yucca fire roll. Already dry and ready to go.

I would think palmetto would have lots of good fibers around the base. If you can find leaves which have fallen off and rotted down to the fibers that should work well. Rotted okra stalks and canna stalks have a lot of good fibers, too. I'll bet most big-stalked plants would be the same, so check whatever grows in your area.