The strong Lonely Runner Conjecture

Let $m$ be a positive integer, let $d$ be a parameter, and let $v_1,\dotsc,v_m\in\mathbb{R}_{>0}$ satisfy $\dim_{\mathbb{Q}}(v_1,\dotsc,v_m)\geq d$. The strong Lonely Runner Conjecture. There exists $t\in\mathbb{R}$ such that

$$\frac{1}{m+2-d}\leq\{tv_i\}\leq\frac{m+1-d}{m+2-d},\qquad 1\leq i\leq m.$$

This strengthens the Diophantine-approximation formulation of the Lonely Runner Conjecture by allowing arbitrary positive real velocities with a prescribed rational dimension. The source gives no resolution evidence.