I just found out why I wasn't able to create all shapes: the shapes depend on the emotion the sim is feeling. Since I did nearly all my clay modeling in my Inspiration room, I was severely limited in which shapes I created.
The list of shapes that can be created according to mood is: (unshaped means the original blob, which does not instill emotion nor have an environment score)
If Fine: Bunny, Llama, Stalks, Bowl, or unshaped
If Playful: Bunny, Llama, Grid, or Stalks
If Flirty: Bust, Tower, or Grid
If Confident: Bust, Bunny, Llama, or Stalks
If Focused: Bust, Geometric, Teapot, or Tower
If Inspired: Bunny, Geometric, Teapot, Tower, or Bust
If Happy: Bunny, Llama, Stalks, or Bowl
If Energized: Bunny, Geometric, Teapot, Llama, Bust, or Tower.
If Angry: Stalks, Bowl, Ripped, or unshaped
If Bored: Bunny, Stalks, or unshaped
If Tense: Stalks, Bowl, or Ripped
If Sad: Stalks, Bowl, or unshaped
If Embarrassed: Bunny, Stalks, Bowl, Llama, or unshaped
If Dazed: Grid, Stalks, or Ripped
If Uncomfortable: Bunny, Stalks, Bowl, Llama, or unshaped