Yes, very happy to discuss; my email is raph.levien at the mail service operated by Google.

I think my approach may be less difficult, as it's based on accepting numerical errors when curves are within epsilon of each other. Thus, a lot of the guts of my algorithm is computing bounds and geometric intervals (adapting some ideas from North's master's thesis[1]). I'm I'm not yet convinced that precise orientation is even possible with cubics.

[1]: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=...