The asymptotic advantage conjecture for distinct unit-fraction solutions

Let $f^*(k,-1)$ be the least board size for which Maker can force a solution with distinct variables in the Maker–Breaker game for the equation $1/x_1+\cdots+1/x_k=1/y$, and let $R^*(k,-1)$ be the least positive integer $n$ such that every two-colouring of $[n]$ contains a monochromatic solution to this equation with $x_1,\ldots,x_k$ distinct. Asymptotic advantage conjecture.

$$\lim_{k\to\infty}\frac{f^*(k,-1)}{R^*(k,-1)}=0.$$

The corresponding limit is known without the distinctness condition, but no comparable lower bound for $R^*(k,-1)$ is known; the authors conjecture that Maker can likewise obtain an asymptotic strategic advantage when the variables must be distinct.