Is there a static substance that reflects loose neutrons? I thought that the choices for a substance were either to let the neutron pass through, or to absorb the neutron

Yes [1]. Beryllium is, I believe, the material of choice (although comes with its own problems, e.g. stupidly toxic dust)

[1] https://en.m.wikipedia.org/wiki/Neutron_reflector

If you're already working with plutonium, whose dust is also very, very toxic (in addition to being radioactive), the additional danger of beryllium doesn't seem so great in comparison.

I routinely handled beryllium for a couple of years as it is present in certain electronic RF power amplifiers. It’s perfectly safe in solid form. If you drill it or smash it, a different matter!

Plutonium, not so much.

I knew a software engineer who made a lot of money in a startup and bought himself an ultralight bike of titanium and beryllium. They ceased the beryllium parts at the Canadian border and I don't think he ever managed to get them released to him.

I think only about 2% of the population is sensitive to beryllium. I was in a beryllium monitoring program (yearly blood tests) at work. A few coworkers are sensitive, one getting really sick.

Beryllium's also used as a neutron multiplier.

I remember reading somewhere that water slows neutrons down enough to allow for a much lower critical mass.

I think it's in mentioned in Richard Feynman's account of his time in Loa Alamos in 'Surely you're joking Mr Feynman'.

Not just any water, only https://en.wikipedia.org/wiki/Heavy_water has that property.

Heavy water is more effective, but light (ordinary) water moderates neutrons too. That's how light water reactors work: https://en.wikipedia.org/wiki/Light-water_reactor

google “demon core” for los alamos beryllium reflector hijinks gone awry.

Moderators reflect and slow down neutrons so you get a controlled reaction: https://en.wikipedia.org/wiki/Neutron_moderator

Beryllium, amongst others.