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In 2015, Campbell et al. presented spectroscopic laboratory gas phase data for the fullerene cation, ${{{\rm{C}}}_{60}}^{+}$, that coincide with the reported astronomical spectra of two diffuse interstellar band (DIB) features at 9633 and 9578 Å. In the following year, additional laboratory spectra were linked to three other and weaker DIBs at 9428, 9366, and 9349 Å. The laboratory data were obtained using wavelength-dependent photodissociation spectroscopy of small (up to three) He-tagged ${{{\rm{C}}}_{60}}^{+}\mbox{--}{\mathrm{He}}_{n}$ ion complexes, yielding rest wavelengths for the bare ${{{\rm{C}}}_{60}}^{+}$ cation by correcting for the He-induced wavelength shifts. Here we present an alternative approach to derive the rest wavelengths of the four most prominent ${{{\rm{C}}}_{60}}^{+}$ absorption features, using high-resolution laser dissociation spectroscopy of ${{{\rm{C}}}_{60}}^{+}$ embedded in ultracold He droplets. Accurate wavelengths of the bare fullerene cation are derived from linear wavelength shifts recorded for ${\mathrm{He}}_{n}$ ${{{\rm{C}}}_{60}}^{+}$ species with n up to 32. A careful analysis of all of the available data results in precise rest wavelengths (in air) for the four most prominent ${{{\rm{C}}}_{60}}^{+}$ bands: 9631.9(1) Å, 9576.7(1) Å, 9427.5(1) Å, and 9364.9(1) Å. The corresponding bandwidths have been derived and the relative band intensity ratios are discussed.