My mom had a cable knit sweater with a stand-up collar totally uncomfortable. I volunteered to fix it for her. I don't have a before picture, but I found something similar on the internets.
What I did was to put a plate on the neckline and make a trace. Cut it and sewed a faux leather bias tape in matching color.
I had trouble in the connection, so I used textile adhesive. I find it convenient in those cases.
My mom can now wear it enjoining the new neckline.
Thanks for reading!