FLS generating-series correspondence conjecture for lambda-class invariants

Let $C$ be a curve class, let $g_0$ be fixed, and define the FLS generating series

$$\mathcal{R}^{FLS}_{g_0,C}=\sum_{g\geqslant g_0}\langle \lambda_{g-g_0};\mathrm{pt}^{g_0-2}\rangle^{FLS}_{g,C}u^{2g-2}.$$

Let $R^{FLS}_{g_0,C}(q)$ denote the corresponding refined tropical FLS generating series, and set $q=e^{iu}$. FLS generating-series correspondence conjecture. Through the change of variable $q=e^{iu}$, one has

$$\mathcal{R}^{FLS}_{g_0,C}=(-1)^{g_0-1}R^{FLS}_{g_0,C}(q).$$

The source states that this correspondence is known for primitive classes and for all curve classes when $g_0=2$; in conjunction with the established point-insertion multiple cover formulas, it would imply the multiple cover formula for FLS invariants with a lambda-class insertion.