I think Pekka is right. If the camera samples above the peak wavelength, and it is a grey body, then an emissivity of 1 seems to be always conservative.
I'm still not entirely sure how the effective exponent works in the instrument software, but I did a calculation similar to Pekka's, if a little simpler: For a given temperature, I found the value of the Planck curve at the camera sensitivity (say 10 µm). Then I found the temperature needed to give the same value from a Planck curve scaled by an emissivity. Finally, I calculated the power using the new temperature and the same emissivity. The temperature is always higher for a lower emissivity as expected. The effect of the emissivity compensates somewhat in the power calculation, but like Pekka, I also found the net effect is positive in all the cases I tried. It's obvious from the curve that the temperature should be higher, but it's not obvious to me that the reduced power from smaller emissivity would never compensate, but that appears to be the case if the peak wavelength is shorter than the sampling wavelength, which is the case in these experiments. I also tried the calculation for much lower values of emissivity, and the calculated power was higher in every case. As I said, the actual effect for all emissivities could be determined with a bit of effort, and the results do favor the authors. But it's not as simple as arguing the calculated temperature is higher if the emissivity is lower as some (including the authors) did, nor as simple as arguing the calculated power is lower because of lower emissivity, as others did. The two effects compete, and it's the net effect that's important. So, the only way the camera could give an overestimate of the power is if the emissivity has some kind of strong wavelength dependence, and I rather doubt a material exists that would give a factor of 3 or more error. So, the upshot is that I can't explain the power gain with an error in emissivity in either experiment. I conceded as much for the March experiment from the beginning, where they measured the emissivity, and that is presumably the more significant run anyway. Even so, I would not be satisfied with this kind of indirect and complex route to a power calculation when flow calorimetry would be far more direct and accurate, even if experimentally more difficult. Still, you can buy tube furnaces with the insulation and cooling lines already set up, and it would not be difficult to adapt such a thing for Rossi's purposes. A big advantage of flow calorimetry is that you can integrate the heat in a very visual kind of way, by collecting, or even circulating the cooling water, thereby raising the temperature of a known volume of water in a 1000 L tub, say.
