James,
Wow, a teacher of writing? That's very cool.
I think it's absolutely possible to develop both sets of skills (technical and creative).
How? Trelawny will probably have her own wonderful ideas, but for creative writing, I would start by writing every day. You know, the kind of free writing that just spills out of you when you are not thinking a lot about what words to say. That is where your truly good ideas lie.
Of course, you can take lots of classes and they help, but for me, I began to see the most progress when I dedicated time each day to writing. I like to write with a pen and a journal because I feel more connected to the page that way. But you can type on the computer if that works better for you. Just keep writing!