Planar 3-uniform hypergraph analogue of the Boots–Royle–Cao–Vince conjecture

Let $\mathcal{H}$ be a planar $3$-uniform hypergraph on $n$ vertices, and let its shadow be the graph obtained by replacing each hyperedge by the edges joining its pairs of vertices. Let $K_2+P_{n-2}$ denote the join of $K_2$ and the path $P_{n-2}$. Planar hypergraph spectral-radius conjecture. For sufficiently large $n$, the $n$-vertex planar $3$-uniform hypergraph of maximum spectral radius is the unique maximal hypergraph whose shadow is $K_2+P_{n-2}$. This is proposed as an analogue of the planar graph extremal conjecture; the supplied text gives no resolution.