Explicit projector formula for spinor tensor products

Let $\lambda=(\lambda_1,\ldots,\lambda_p)$ be a Young diagram with $\lambda_1+\lambda_2\leq 2k$ and $p\leq n$. Let $S$ denote the spinor object, let $\tilde y_\lambda$ be the minimal idempotent associated with $\lambda$, and let $\tilde P_+(\lambda_i)$ and $\tilde P_-(\lambda_i)$ be the idempotents determined by the parity of $\lambda_i$. Define

$$b=(\lambda_1+1/2,\ldots,\lambda_p+1/2,1/2,\ldots,1/2).$$

The explicit projector formula. The idempotent projecting $\lambda\otimes S$ onto the simple object indexed by $b$ is

$$p^{\lambda S}_b=(\tilde y_\lambda\otimes id_S)(\tilde P_1(\lambda_1)\otimes id)\cdots(id\otimes\tilde P_p(\lambda_p))(\tilde y_\lambda\otimes id_S),$$

where

$$\tilde P_i(\lambda_i)=\begin{cases} \tilde P_+(\lambda_i),&\lambda_i=0\mod 2,\\ \tilde P_-(\lambda_i),&\lambda_i=1\mod 2. \end{cases}$$

This would give an explicit construction of the remaining projector in the inductive construction of simple objects in the orthogonal modular category. The source says that the statement is hoped to be proved in the future, and provides no resolution.