One thing about symbolism (and this is totally my opinion based on my own writing experience)... I feel like you're better off not "trying" to add it to your story, at least in first draft, or it may seem forced.
Instead, you just write the story and let your subconscious throw stuff in there that turns out to be rich, deep symbols. Sometimes you recognize them as such when you're writing, most often you don't.
Where the storyform comes into it is, you use the storyform to align your conscious ideas of the story to the narrative your subconscious is giving you. If you manage to do that, I think the chance of you ending up with symbols that relate to the meaning of your story is greatly increased. (I feel like your subconscious almost can't help throwing these symbols in there, because symbols and narrative are its language.)
In any case, when you're finished the first draft you can look over it and see what symbols came out, and decide then what to do with them (maybe strengthen some, maybe remove others that no longer fit, etc.).
Just my two cents. Maybe I'm just lazy and would rather not worry about symbols when there's enough other stuff to worry about in writing! .