Boy, i can relate to the engineer brain trying to see if there's any creative in there...
First, I think you already know that there is. You're artistic - moreso than you give yourself credit for. You've already pushed beyond things I never knew you'd be into.
Second, I can only speak from experience here, so here's what I've discovered about my own artistic journey:
When I finished the last guitar, I was proud of the execution and the outcome, for sure. But it was so sentimental, it HAD to be done well. It meant too much to ME personally to allow it to be anything less than the absolute best I could give. Honestly, that kinda drained me. Once it was done, i wanted a project I could just do for fun. Just goof around with things I haven't really tried before. So I decided to build the table.
The best part about building that table was that I didn't care about how it looked. Now, that sounds weird, but it's true. I didn't give a dang how it looked. That's not to say I didn't want it to look good. No, it HAD to look GOOD. But i didn't care how it got there or what it arrived at. The end result of the piece did not matter to me. It had to be QUALITY, but what it looked like didn't matter.
What this meant for me was that I was FREE from all predisposed ideas about how it had to look for ME. It wasn't FOR me. It was for the sake of doing something creative and I was absolutely free to go wherever the vision took me. I wasn't constrained by my own tastes or my wife's tastes or my opinion of what someone else thought it should be. It just had to be what i had in mind. And what I had in mind could literally be ANYTHING i wanted to do. I didn't care. It didn't have to fit anything except what i was willing to try.
It turned out ugly, in my opinion. It's the ugliest thing I've ever built on purpose. I'm proud of the execution. It looks good. But it's an ugly piece that I do not want in my home. I'm not the least bit sentimental about it. I'm not attached to it at all. I am happy with the outcome - it's built well - it came out exactly as I had envisioned. The execution is as fine as anything else I've built. And, it exercised a part of me that I didn't know I had - which was the whole point of the project in the first place: to see if i could do something for the sake of art.
That freedom from my own prejudice and aesthetic opinion is the reason it did. If i had allowed myself to get attached to it, or to care about how it looked, then I wouldn't have built what I did. It would've been very different. It would've been precise, rectilinear and very boring. Not artistic. Just another table. Not unique.
I firmly believe that you have to set yourself up for such a free expression to really explore your capability. Pick a technique you like (in my case, the table was because i wanted to do some sculpted joinery) and form a vision ... just pick something you'd like to create in your mind and then set about creating it. You've built enough things by now to know how to solve all the engineering parts so don't think about those things at all ... pick a vision, then you'll engineer solutions to execute that vision.
In the case of the table - i knew i wanted sculpted joinery for the branches - that was as far as I thought it until it came time to fasten the limbs on. Then I had to engineer a little - to make sure the joinery was sound - soon as I'd solved it, engineer was back out and artist was back in -- back to the shaping, fitting to my vision -- no more math, no more measuring, no more engineering. Just remove the parts that aren't the thing I had in my mind.
It was the most freeing project I've ever done ... I've never felt more unconstrained in my life.