I would just do it as a standard fill stitch - nothing fancy.
Run a sample, show customer, get approval, run job.
Unless the customer says anything about the pattern in the fill, I wouldn't waste time trying to get it the same.
Is the pattern in the artwork for anything else, letterhead, signage etc? If not, don't sweat about matching it to the item supplied.
That fill looks a lot like the fills Capital Automation, another software package, does with default settings (attached).
You will spend waaaay too much time trying to get a match - run sample, adjust settings, repeat......
The only thing critical, to me, would be density of the fill, so you can put your text over the top without issues.