I would suggest 'Single- and double-slit diffraction of neutrons" by Zeilinger, Gahler, Shull, Treimer, and Mampe, Reviews of Modern Physics 60(4), 1067-1073 (1988). If I might quote the abstract:
The authors report detailed experiments and comparison with first-principle theoretical calculation of the diffraction of cold neutrons ($\lambda \approx$ 2 nm) at single- and double-slit assemblies of dimensions in the 20—100
$\mu$m range. Their experimental results show all predicted features of the diffraction patterns in great detail.
Particularly, their double-slit diffraction experiment is its most precise realization hitherto for matter
So, single and double slit experiments with neutrons have indeed been done, and indeed show just what would be expected.
Here's a brief description of how the experiment worked. They used neutrons from a reactor, which were brought down to room-temperature thermal energies using heavy water. They let those out through a collimator to make a beam. To make the beam monochromatic, they bent it through a quartz prism and selected one wavelength using a a slit. They verified the energies using time of flight (I think using a beam chopper). To produce diffraction, they used a tiny double slit with a spacing of 0.1 mm. At a distance of 5 m from the double slit, the spacing of the fringes was about 0.1 mm, and they had to make the graph by slowly moving the detector across the fringes and measuring a count rate at each position.