@Catllar some rayons are such a pain. I cut nearly everything on the flat which I started doing when I sewed knits because no matter how careful I was I'd always end up with one perfect side and one slightly off grain side. Now I'm always on grain.
I have one rayon in particular that is pretty bad. I made SA Ethel Designer pants from it and the leg hems are a bit wonky. Unfortunately I still have some of that fabric and I decided to use some of it for a muslin of the SA Vicki Top but because of the points in the pattern pieces it was quite messed up and I ended up throwing it away.
I have had some rayons that behave quite well. many rayon fabrics that behave fine though and others that are terrible. Same issue with some tencel fabrics where they seem almost bubbled. I'm pretty sure rayon was responsible for me giving up zippers back in the early 2000s.
Some people recommend using starch but the one time I tried it I hated the mess it made. Maybe I did it wrong.
I like the rayon ... are you doing something with the border?