By training, schooling, and experience I am an Engineer, Metrologist (art and science of measurements) and an amateur facetor. I can contribute little to the Arts - I suppose I am to "structured".
John,
When I was in engineering school (BSME/BSCS) I too discovered that I
was, shall we say, “art-challenged”. 
During the required art
classes, I kept trying to pull out my rulers, protractors, etc.,
frustrating both the instructors and myself. I think part of it is
just an “occupational hazard”, with the other part being that part of
our personality that led us to engineering in the first place. We’re
trained to be ordered, precise, even somewhat “rigid” in our thinking
and methods – great for engineering, faceting, stone-setting, etc.,
but fairly inhibiting when it comes to freeform, non-symmetrical
design.
I’ve learned to compensate in a couple ways. First, when I sit down
to do the design phase of a new project, I have a glass (or two) of
wine or beer to lubricate the wheels in this thing I call a brain.
While this is less than a functional solution for those in the group
who are professionals, for me it helps lessen that initial inhibition
enough for me to try something new. Second, and at the risk of
reigniting the “Copied/Stolen Designs” thread, I maintain a scrapbook
of designs that are free-flowing, abstract, organic, etc., that I use
for inspiration. Rather than copying them, I sit there – with my
glass of wine in hand – and thumb through the pages for a while
until I can get a sense of the mindset. Then I close it, take out my
design notebook, pour the second glass of wine, and let the muses
take me where they will.
My projects still tend to be on the more “structured” side, but I can
look through my portfolio and see a gradual improvement as time has
passed. For me it’s a journey taken one faltering step at a time and
savored along the way.
Warm Regards,
Shawn