Thank you all for your wisdom!
I could not find any daylily seller that is near New Orleans, but I did go out and get a "Pardon Me" daylily from a local nursery. It is listed as a diploid and I suspect my plant is indeed a stella (thanks, DogsNDaylilies!), which should also be diploid. I will try crossing them to see if I get viable seeds. I've also moved my plant to the side of the balcony where it will get more morning sun and less afternoon sun so it won't get as hot, but overall will get less light. I'll probably bring it inside once the summer kicks in.
I'll post an update in a few weeks. Thanks again!