Yes,
Primrose is too cutesy for me. I think it sounds twee and stuckup.
Prim is annoying.
Rosie is fine.
Rose is better.
I think
Primula (genus name of the flower) or Primarosa would be nicer by about a factor of ten.
I think the second worst thing about
Primrose (after the word prim in it and the sound of "prim rows") is the sound, the feeling of saying it - the "pr" plus "mr" is so ... pursed-lippy. Like a word a boudoir photographer would tell the subject to say, to get a big fat pout in the picture.
Primrose. Mwah!
Okay, so I've thought about it too hard. But it gags me. I didn't even realize it was in Hunger Games, I thought it was just a flower-name trend gone wild sort of thing.
I favor just plain
Rose, from your list.
Rosemary is not bad either. Actually any of them are okay with me, except
Primrose.
Rose combines well with many short names IMO.