Hm, it sounds like it could be 1) a pinched nerve as it exits the spine or 2) pinched while in the spinal canal. The former would be the typical picture, while the latter would occur if there is still further instability.
In spondylolisthesis, patients may also have disk issues occurring due to the fact that it has to withstand compression + shear stress from the slippage with degeneration from the disease process. This may cause flexion-based pain due to disk prolapse, and may be bilateral/unilateral. The anterior pelvic tilt is what keeps the defect stable, as it changes the center of gravity. When the pelvic tilt is lost, the vertebrate can further slip forward causing pain from further shear stress as far as I understand it.
But hyperextension may also cause further pain by aggravating the impingement of the nerve roots as it exits the spine via the foramina, and may present unilaterally. This is the typical of spondy.
In any case the pain would be radicular in nature regardless of whether the nerve is impinged in the spinal canal or foramen.
My hunch is that you may have impingement of the nerves within the canal due to the slippage from a disk issue which is also present, which becomes worse as you bend forward. Was an MRI done to exclude disk pathologies which may be present at the same time? The problem here is that the pain can be due to both flexion or extension, with different causes within the same disease.
Sorry that I can’t give a more informative answer, as I did not have any experience with spondy patients during my orthopedics posting; they were all prolapsed disk patients. Do ask your specialist, as spondy for the most part is postgraduate material in a UK-based medical education. And don’t forget to monitor for neurological deficits: check your ability to 1) toe walk, 2) heel walk in both legs. Good luck, the sight of people with radicular pain just sucks.