Totally agree that it’s a mistake to tie personhood to biology. Biology is measurable, and personhood is a linguistic construct design to dehumanize those who look different.
As far as your non-binary suggestion, it’s not practical, as our legal system grants certain rights to “persons” and other rights to “citizens.” Historically, we’ve denied “personhood” to minorities, women, and the unborn. Rather than argue what’s a person and what’s not, let’s just agree that it’s stupid to talk about some ambiguous “personhood” requirement and just make laws based on whether or not someone is biologically human or not.