  A key to understanding unconventional superconductivity lies in unraveling
the pairing mechanism of mobile charge carriers in doped antiferromagnets,
yielding an effective attraction between charges even in the presence of strong
repulsive Coulomb interactions. Here, we study pairing in a mixed-dimensional
(mixD) $t-J$ model, featuring robust binding energies -- despite dominant
repulsive interactions -- that are strongly enhanced in the finite doping
regime. The single and coupled mixD ladders we study, corresponding to bilayers
of width $w\leq 2$, feature a crossover from tightly bound pairs of holes
(closed channel) at small repulsion, to more spatially extended, correlated
pairs of individual holes (open channel) at large repulsion. We derive an
effective model for the latter, in which the attraction is mediated by the
closed channel, in analogy to atomic Feshbach resonances. Using density matrix
renormalization group (DMRG) simulations we reveal a dome of large binding
energies at around $30\%$ doping, accompanied by a change of the Fermi surface
volume and a crossover from extended to tightly bound hole pairs. Our work
provides a microscopic theory of pairing in the doped mixD system with dominant
repulsion, closely related to bilayer, Ni-based superconductors, and our
predictions can be tested in state-of-the-art quantum simulators.
