A supercongruence for a truncated hypergeometric series with parameter r

Let $r$ be a positive integer and let $p$ be a prime with $p>2r+1$. The supercongruence.

$$\sum_{k=0}^{p-1}k^r\left(k+\frac{1}{p+1}\right)^r\frac{\left(\frac{1}{p+1}\right)_k^{p+1}}{k!^{p+1}}\equiv 0\pmod{p^4}.$$

This is one of three proposed strengthenings related to the paper's earlier supercongruences; its status is conjectural.