Surjectivity conjecture for the annular skein map onto the centre of $H_{n,p}$

Let $H_{n,p}$ be the Homfly skein algebra with $n$ positive and $p$ negative boundary points, let ${\cal C}$ be the skein of the annulus, and let

$$\psi_{n,p}:{\cal C}\longrightarrow Z(H_{n,p})$$

be the algebra homomorphism obtained by placing an annular skein around the identity tangle. Surjectivity conjecture. The image of $\psi_{n,p}$ is the whole centre of $H_{n,p}$:

$$\operatorname{im}(\psi_{n,p})=Z(H_{n,p}).$$

For $p=0$, the analogous result is known in the generic case from the description of the centre using symmetric polynomials in the Murphy operators. The conjecture asks whether the same central-generation property holds for all $H_{n,p}$.