The detectors of the Ultraviolet Spectrographs (UVS) on Voyager 1/2 are recording a background intensity that was earlier assigned mainly to disintegrations in the radio-isotope thermoelectric generator and systematically subtracted from the signal to infer photon counting. Here, we show that it arises instead from galactic cosmic rays (GCRs). We show the GCR flux measured by UVS on Voyager 1 from 1992 to August 2013, and by comparing to data from the GCR dedicated detectors, we estimate the energy range responsible for this UVS signal, which is around 300 MeV, and the response of UVS to the GCR anisotropy. After the abrupt jumps of May and August 2012, the count rate has been only slightly fluctuating around a constant value. However, comparing it to the data from the Low Energy Charge Particle Experiment (LECP) and the Cosmic Ray Subsystem (CRS) shows that those small variations are only responses to a varying anisotropy and not to a flux change. Taking advantage of the similarity in energy range to one of the products of the CRS instrument suite, we use the ratio between the two independent signals as a proxy for the temporal evolution of the GCR spectral slope around the 300 MeV range. We show that this slope remained unchanged since August 2012 and find strong evidence that it will no longer vary, implying the end of the heliospheric modulation at those energies, and that Voyager 1 at this date is near or past the heliopause. The origin of this unexpectedly narrow and stagnating inner heliosheath is still unclear, and we discuss the potential effects of low solar wind speed episodes and subsequent self-amplified charge-exchange with interstellar neutrals, as a source of deceleration and collapse. We suggest that the quasi-static region encountered by Voyager 1 may be related to such effects, triggered by the strong solar-maximum variability. This did not happen for Voyager 2 due to its trajectory at an angle further from the heliosphere axis and a later termination shock crossing. The existence on the upwind side of a mixing layer formed by charge transfer instead of a pure plasma contact discontinuity could explain various Voyager 1 observations.