The $\gamma$ radiation produced in cosmic-ray and gas interactions has been used to probe the local cosmic-ray spectrum in several clouds to distances of about 1 kpc around the Sun. Early measurements made with Fermi LAT data were found in good agreement with the proton and helium cosmic-ray spectra reaching the Solar System, given the 10-15% uncertainty in target gas mass that is inherent to HI line observations. The local cosmic-ray uniformity has recently been challenged by the finding of a significant loss of particles in the nearby Eridu cirrus. We have revisited the $\gamma$-ray emissivity spectrum one would expect per gas nucleon from hadronic and bremsstrahlung emission using the latest cosmic-ray spectra inferred near the Sun, outside the heliosphere. We have also used improved photon production spectra in nucleus-nucleus interactions. We find that, because of the current uncertainty in the $\gamma$-ray yield per nuclear interaction, one cannot conclude whether the average cosmic-ray spectrum measured within $\sim$1 kpc from the Sun is comparable or superior to that inferred just outside the Solar System, nor whether the low cosmic-ray flux pervading the Eridu cirrus is consistent or not with the flux reaching the Sun. The Eridu cirrus and the Sun both lie in a hollow valley of the local interstellar medium. We show that the cosmic-ray flux in Eridu is about half that observed in two other more massive clouds that flank the valley.