I regularly read ArXiv for reports on the experimental limits on Fifth Forces. But this on I missed up to now. Neutron Scattering is regularly performed on every material under the sun, and in neutron scattering, scientist clearly see point like scattering from the strong force of a nucleus, giving very clear scattering from a collation of femtoscopic points. What scatterers don't see is any scattering from long range $1/r^2$ type columb forces. This clearly limits strongly any fifth force felt by neutrons. Unfortunately the one paper producing limits on fifth forces from neutron scattering is the R. Barbieri and T.E.O. 1975, and they start there calculation from a parameterised best fit to scattering from a Russian experiment done in 1966. Another words, the experiment hasn't been done with a good level of statistical checking. However thinking about its very clear that a massless force with strength 100-1000 time weaker than the electromagnetic force is clearly and obviously excluded by neutron scattering experiments, it would stand out like a sore thumb.
Where does this level fifth forces in general, and in particular our axial force. First B-L forces which act between all known particles are clearly excluded, saying goodbye to B-L chameleon force. In describing our axial force we could not see any way to pin down the particular charges on a proton or neutron, and w guessed at +1/2 for a proton and -1/2 for a neutron as that would be symmetrical and prevent proton decay. However we cannot rule out a charge on 0 on a neutron and 1 on a proton. Thus our axial force remains viable with these charges, we still have requirement that some light charged scalar or vector fields (mass around a few eV) exists to prevent Fermi energy from becoming too great. With both light scalars and neutrinos as light charged fermions under a fifth force, chameleon like behaviour should screen any axial force down to the nanometer scale, guaranteeing that it would not have been observed in existing experiments.