  We present a shuffle realization of the GKLO-type homomorphisms for shifted
quantum affine, toroidal, and quiver algebras, thus generalizing its rational
version of arXiv:2104.14518 and the type A construction of arXiv:1811.12137. As
an application, this allows us to construct large families of commuting and
q-commuting difference operators, in particular, providing a convenient
approach to the Q-systems where it proves a conjecture of arXiv:1704.00154.
