Recent experiments have explored the use of a free-electron laser (FEL) as a buncher for a microwave two-beam accelerator, and the subsequent driving of a standing-wave rf output cavity. Here we present a deeper analysis of the longitudinal dynamics of the electron bunches as they are transported from the end of the FEL and through the output cavity. In particular, we examine the effect of the transport region and cavity aperture to filter the bunched portion of the beam.