Oh, your going to love this theory.
https://fondationlouisdebroglie.org/AFLB-222/MARK.TEX2.pdf
In summary, There is a way to model electrons as a twisted self enclosed em field.
A decent digest summary of the paper is this video
https://www.youtube.com/watch?v=hYyrgDEJLOA (Huygens Optics: Are Electrons made of Light? )
Analysing hand-me-down neutron events from indirect collisions isn't quite as useful.
Spallation generation: High-energy protons (~800 MeV) hit a heavy target, releasing a wide spectrum of fast neutrons up to hundreds of MeV. These are then moderated down to useful energies for experiments.
It’s not the LHC, sure. But I don’t see any reason (apart from “why bother”) why they can’t do spallation in Geneva. OK maybe there’s a cooling problem…
But neutrons can't go around a tube being guided by magnetic fields
There’s an ultra cold neutron source at Paul Scherrer that is used to measure if the neutron has an electric dipole moment. This is complementary to high energy experiments.
Of course more experimental data is a good thing, but in this case it doesn’t seem obvious that it would lead to anything really new.
When that happens is less understood, hence the discrepancies you mentioned.
The comment I replied to talked about "new physics". That's a term that's used in physics to describe physics beyond the Standard Model. Better experimental data about neutron internals could certainly help constrain the neutron lifetime, but that would be likely to be experimental constraints on existing physics, not new physics in the sense that the term is normally used.