The honest truth is there's just a certain acceptable level of jank in a scientific lab.

Not everything needs to be measured to a high precision to be useful, and it's always a balance of how much effort you want to expend versus how useful that extra accuracy/precision is.

If all you care about is "when you're getting close to a critical mass, your instruments will look like this," you don't care that you have a wide swing in your data. You just want to show a difference from baseline.

Sometimes science doesn’t have to be precise to demonstrate a result.

Consider trying to measure feedback from a microphone and speaker. You don’t have to be an expert to know that there’s a quick change in system behavior when the microphone gets too close to the speaker.

If the goal is to collect precise data and use it after the experiment to draw conclusions, update a model, etc. then sure.

If the goal is to demonstrate to observers how the neutron output (reaction rate) increases as the reflectors are moved closer together over the source, then that isn't really necessary.

This seems more like an incredibly dangerous version of a demonstration you might see at an interactive science museum or a classroom. You don't need precise measurements to demonstrate the relationship between two phenomenon.

I think it was more about being able to understand/read what the measurement devices were showing. The exact distance probably wasn't as important as the criticality could also vary with other variables (e.g. geometry).

As in, you're trying to understand the situation as "shouldn't they have precisely nailed down all the parameters, if the goal is to measure when X starts happening". But it seems Slotin was more demonstrating "this is what you're going to see on the monitors when stuff is close to going boom". It wasn't about "this specific distance is a safe gap" and more "here's how you can tell whether the gap is safe".

He was about to be reassigned out of the lab, and was demonstrating equipment to his designated successors.

This is just proving 'move spheres closer means more neutrons'. It's something you quickly show someone to explain what you are going to do. The people watching will then get most of the same ideas you are suggesting, and figure out how to design a proper experiment around it.

Presumably the experiment to be done later is about characterizing different cores. They had already done it for this core, and wanted to teach the principles to others.