Let ${\sf RT}^n_k$ denote the statement "For all infinite sets $Z$ and functions $c : [Z]^n \to k$, there is an infinite subset $H$ of $Z$ such that $c$ is constant on $[H]^n$.”.
The infinite Ramsey theorem states that "For all $n,k \in \mathbb N^+$, ${\sf RT}^n_k$ holds.". It is well-known that Ramsey's theorem implies Kőnig's lemma over $\sf ZF$, so some form of choice is necessary to prove it (for example, "Every Dedekind-finite set is finite." suffices).
In the paper by Forster and Truss, the authors show that the statements ${\sf RT}^n_k$ are all equivalent for all $k \in \mathbb N \setminus \{0,1\}$, where $n$ is fixed, over $\sf ZF$. More interestingly, they also show that (with a very interesting proof) for all $n_1,n_2,k_1,k_2 \in \mathbb N$, where $n_1 \geq n_2 \geq 1$ and $k_1,k_2 > 1$, we have ${\sf RT}^{n_1}_{k_1} \implies {\sf RT}^{n_2}_{k_2}$, over $\sf ZF$.
However, the authors point out that they were unable to show the reverse implications (the upward implications for the upper index) over $\sf ZF$, and they also note that they think these implications are unlikely to hold.
My question is: Are there any new results regarding these reverse implications? Thank you.