To the family of nonisospectral variable-coefficient higher-order Korteweg-de Vries equations a new family of nonisospectral variable-coefficient higher-order modified Korteweg-de Vries equations depending on a parametric function eta (t) is constructed. They are connected by an eta ²-dependent Miura transformation. A Backlund transformation is also established. Furthermore, the gauge transformation previously proposed by the authors is applied to this Backlund transformation. For a fixed eta (t), this enables one to derive an autoBacklund transformation for the families of non-isospectral variable-coefficient higher-order eta ²-dependent modified Korteweg-de Vries equations and non-isospectral variable-coefficient higher-order Korteweg-de Vries equations, respectively. As an illustration, three generations of explicit solutions of the non-isospectral second-order variable-coefficient Korteweg-de Vries equation are presented.