Oka's cyclic fundamental-group conjecture for mixed projective curves

Let $f:\mathbb C^3\to\mathbb C$ be a non-degenerate, strongly mixed homogeneous polynomial of polar degree $q$, and let

$$V=\{[\mathbf z]\in\mathbb P^2\mid f(\mathbf z,\overline{\mathbf z})=0\}$$

be the associated smooth projective mixed curve. Let $F=f^{-1}(1)\subset\mathbb C^3$ be its Milnor fiber.

Oka's conjecture. The Milnor fiber $F$ is simply connected. Equivalently,

$$\pi_1(\mathbb P^2\setminus V)\cong\mathbb Z/q\mathbb Z.$$

For holomorphic homogeneous polynomials, the corresponding fundamental-group statement follows from the connectivity theorem for Milnor fibers. Mixed polynomials lack a general connectivity theorem, although the author reports no examples violating the holomorphic-case connectivity and gives supporting examples for this conjecture.