New runner removal theorems for the cyclotomic Hecke algebras of type $G(r,1,n)$

For the Iwahori-Hecke algebras $\mathcal H_q(\mathfrak S_n)$ of the symmetric group $\mathfrak S_n$ at a primitive $e$-th root of unity, James and Mathas proved a theorem which relates $v$-decomposition numbers $d_{λμ}^{e}(v)$ for different values of $e$, by adding ``empty runners'' to the abacus di