We present a simulation framework for computing the probability that a single molecule reaches the recognition element in a nanopore sensor. The model consists of the Langevin equation for the diffusive motion of small particles driven by external forces and the Poisson-Nernst-Planck-Stokes equations to compute these forces. The model is applied to examine DNA exo-sequencing in α-hemolysin, whose practicability depends on whether isolated DNA monomers reliably migrate into the channel in their correct order. We find that, at moderate voltage, migration fails in the majority of trials if the exonuclease which releases monomers is located farther than 1 nm above the pore entry. However, by tuning the pore to have a higher surface charge, applying a high voltage of 1 V and ensuring the exonuclease stays close to the channel, success rates of over 95% can be achieved.