Make, learn and talk about needle lace.
I have not tried 6 strand floss. It is very fragile. I doubt it is strong enough. And one tiny break could make a section of the lace unravel itself.
However I have used their Coton a Broder (Broder cotton). It is a single strand, quite soft and very flexible, so it loops well, much softer and more flexible than cordonnet, which is actually a crochet and tatting cotton. Broder cotton comes in a lot of colors but you have to search for a supplier on the internet. It also comes in several sizes. The colors are usually in #12 or #16. The #12 is comparable to pearl 12. The white and ecru come in more sizes, down to #30 and even finer. It is not as shiny as pearl cotton, but doesn't have that highly visible twist.
One strand of embroidery floss is Ok to work needlelace with, but it makes Very soft lace, and has very little "body" and is a bit floppy.
Hi. Quilting threads can be good. I have used the Madeira King Tut and well as a thread called Sulky, not sure of the manufacturer though. But really any thread that is cotton or silk is good. Guttermans silk thread good as well. I don't think I have ever used a linen Thread as I think it wouldn't be strong enough or easy to work with as it can be slubby. Crochet cotton or tatting threads as good although they are quite highly twisted, they are stiffer than others. My purple and pink/green flowers are worked in them. The dark pink one was done in DMC perle 8 although this is a very soft thread, it works well. Depends on what you are making and what you want it for. There are lots of lace suppliers on line who sell all sorts of threads so how about looking at one of them. Jo Firth, Roseground, Makit, Mainly Lace or Church Meadow Crafts are all in the Uk and easy to deal with. And they take credit cards!