It's beautiful! Don' worry about your signature being crooked, that's what makes even more treasured-it's handmade and personal.
Can you try turning the label upside down into a plate or flat surface of salt? Believe it or not, salt will draw out any oils or dirt from cross stitch. Also you can try blotting with club soda but be very careful on getting the club soda onto the colored thread just in case the color bleeds. Use a soft absorbent terry towel.
I used to cross stitch alot and the salt trick was from a class that I took when I was learning how to frame cross stitch work. It worked on a wedding sampler that I did that took a year to complete.
Also, since it is for your bff, I don't see anything wrong with giving it to her early, before the wedding so she can enjoy it.