Last time I found a paper in Graphics Gems titled Solving the Nearest-Point-on-Curve Problem, which transforms the problem into a Bernstein polynomial form. Then an exact solution can be obtained using A Bézier Curve-Based Root-Finder. This is my implementation [1], but it's not very robust for high-degree cases.
At most one instance at start up. Asynchronous creation or lazy creation on first use are two other potential options. Speaking generally, not Unreal-specific.
This was my first instinct as well, which makes sure numbers are adjacent. OP also mentioned this variant as lucidBrot/hexgridspiral in the older post.
http://www.peda.com/grafeq/