I have an intuition that high energy physics, i.e. studying strong nuclear force, should be accessible via low energy neutron beams because neutrons can interact with nuclei without being impeded by electromagnetic forces. It should be possible to bombard different elements with neutrons of low, but varying energies and analyze the resulting cross-sections of particles. Can anyone recommend me any relevant review or experimental articles?
You are right in your thinking. When I was in school we did, and people still do, low energy neutron scattering off heavy (Pb, Os, and many other) nuclei. This was done in the neutron energy range of 2.0 - 8.0 Mev neutrons. The energy levels of the nucleus were found using the $(n,n'\gamma) reaction$. We also measured the nuclear scattering cross-sections as a function of angle. Neutrons were used because, as you pointed out, they interact only via the nuclear force. Studies like these have been done on many lighter nuclei as well. The $(n,n'\gamma) reaction$ is very useful for extracting the energy levels of a nucleus.
If you have access to a science library you can read descriptions of this by looking for academic papers by Marcus McEllistrem or Sally F Hicks. Those papers or the references within should explain all.
If you are interested in the experimental techniques ask a question about them and it will be answered by me or someone on this site.