Stacked two-dimensional materials provide a promising platform for electrically controlling topological electronic states. However, tunneling between layers hybridizes their bands and removes the crossings needed to change topology. We show that this does not always have to be the case. Band crossings and associated Weyl points are topologically enforced in Hofstadter bilayers whose layers experience different magnetic fluxes. When resonant magnetic Bloch multiplets carry unequal Chern numbers, their projected tunneling is topologically obstructed and must vanish at isolated momenta. Sweeping the layer bias through these zeros creates synthetic Weyl monopoles in momentum-bias space that transfer the Chern mismatch. We demonstrate two consequences: a direct transition between insulating Chern phases and a reentrant compensated metal in which Lifshitz transitions bound the metallic window while internal Weyl events reconstruct the band topology. Consequently, the fixed-filling Hall response remains continuous and nonquantized even as integer Chern number is transferred between bands. Berry-flux, TKNN, and interface calculations independently verify the mechanism and its multichannel chiral signature. We outline realizations in Moire and anomalous-Hall heterostructures, establishing flux mismatch as an experimentally accessible route to electrically programmable Chern phases and chiral transport.