Numerical simulations and a simplified model are presented for the dynamics of linear arrays of deformable drops in parallel-wall microchannels. Efficient boundary integral simulations were developed by exploiting the Hele-Shaw far-field form of the two-wall Stokes-flow Greens function. The simulations show a tendency for drops to form pairs at long times. Within each pair, drops are separated by a distance that depends on deformability and wall spacing; the distance between pairs depends on the initial configuration. Under some conditions, the initial pairing of drops is incompatible with the long-time configuration. In this case, the final state is ultimately attained through a pair-switching cascade. We propose a simplified model for the drop dynamics based on a superposition of pairwise hydrodynamic interactions of confined drops. Our simplified model quantitatively predicts the dynamics observed in the full boundary integral simulations. We find that pair formation and the transient pair-switching cascade result from three components of the pairwise hydrodynamic interactions: dipolar and quadrapolar far-field contributions, and short-range hydrodynamic repulsion associated with drop deformation.