If Lycra doesn't agree with you, then try the Cotton Concealer--and you might try a size smaller than you think you need. Let me know if you want to talk about sizing for this particular garment. I've had some experience with it. Perhaps some other guys will chime in, too.
I've suffered from eczema and severe skin allergies all my life. I can't wear synthetic fabrics--only 100% cotton for me. So I originally had strong reservations about binding. Perhaps you can learn something from me?
The nice thing about the CC is its composition. The inner layer is nylon and spandex, but the outer layer is 90% cotton and 10% spandex. Yes, it's a double layer of binding, but it can be great for people with sensitive skin. Lots of guys turn this binder inside out and wear it right next to their skin.
When I first started binding regularly, I had been on T for maybe a month. I was turning the binder inside out, but my skin still couldn't take the 10% spandex. So I wore a wifebeater under the binder. In fact, I was double binding then. The weather was cooler then, so I didn't mind all the layers.
Last week, it was pretty warm in my neck of the woods. I had a new binder, a smaller size, and I wondered if T had sufficiently toughened my skin that I might be able to wear the binder without a wifebeater. I had had an annoying eczema outbreak that hadn't gone away for months, and it was suddenly clearing. So I had hopes.
I wore the binder inside out, right next to my skin, for eight hours. No problems whatsoever. Now I don't bother with the wifebeater.
I would never have thought to try this smaller size if I had been going by the sizing charts. I only bought it because the size I had was clearly too large, so large that only two binders would do the trick. So the CC might be a solution for you. I'll give you all the info I can--just ask.