The Ramsey characterisation by monochromatic line configurations

Let $X\subset\mathbb{E}^d$ be a set. Call $X$ Ramsey if for every natural number $r$ there exists $n$ such that every $r$-colouring of $\mathbb{E}^n$ contains a monochromatic copy of $X$. Write $\ell_m$ for the relevant $m$-point line configuration, and write $\mathbb{E}^n\rightarrow(X,\ell_m)$ when every two-colouring of $\mathbb{E}^n$ contains either a monochromatic copy of $X$ in the first colour or a monochromatic copy of $\ell_m$ in the second colour. The Ramsey characterisation conjecture. A set $X$ is Ramsey if and only if for every natural number $m$ there exists $n$ such that

$$\mathbb{E}^n\rightarrow(X,\ell_m).$$

The forward implication is already known from the characterisation using arbitrary fixed configurations $K\subset\mathbb{E}^m$; the conjecture asserts that line configurations alone suffice for the converse, which would give a simpler characterisation of Ramsey sets.