I investigated a gradient-descent-based concept adjacent to this back in like 2023 [0] inspired by the original 3DGS paper, I was pretty happy with the results I got with back-to-front alpha-blending and polar-coordinate gaussians for variable-curvature brush strokes. One of these days I should add another example gif to the repo besides just the Mona Lisa one that's currently there, but that's the only one I've got at the moment unfortunately.

[0] https://github.com/mkaic/painterbot