I find it interesting that you tend towards SMT solvers instead of gradient descent solvers. Is it because you want to avoid having to specify approximate solution? CAD tools get away with this because the draughtsman is providing the rough starting point.
Also, as a further question? Is it open-source/free software? I couldn't find any links.
I'm currently using SMT for a number of reasons. One issue is that I've found the constraint is often non-convex, and this sometimes causes issues. And yeah, as you guessed, the initialization is also a hard part. With some figures, I've found that gradient descent can find the right solution with a good initialization (or even with just trying a handful of random initializations), but it doesn't work every time, and I wanted to avoid relying on the user to provide a good starting point.
The right thing moving forward might be some hybrid of SMT and gradient descent, especially if an interactive GUI editor comes into the picture. SMT could provide the initial solution, and gradient descent could help when the user manipulates the figure using the mouse.