Calculation of fluorescence quantum yield
After some more reading, it turns out that the protocols suggesting to use the integrated intensity are wrong and it is necessary to correct for the variable wavelength across the emission peak. Würth et al. (2013) provide a description of the correct method. First, they state that


  all fluorescence spectra have to be converted to a (relative) number of photons per unit time


Second, they describe the conversion as discussed in the question:


  the radiometric quantity has to be multiplied with $\lambda/(hc_0)$