Jed, I don't doubt there is an energy release.
To prove LENRs are occurring we should exclude any other (conventional) source of energy.
I see what you mean. The best way exclude a conventional source of energy is to let the thing run and continue to monitor both power and energy output. When the energy output exceeds the limits of chemistry by a wide margin, you know the effect is anomalous. That might be challenging because the energy flow is so low.
It is fairly easy to estimate the limits of chemical energy with a palladium cold fusion cell. You estimate approximately how much energy the fully loaded cathode can hold. I don't know how much energy an LEC could hold -- if any. It would be some sort of battery. I guess the crude approximation would be to estimate how much energy the LEC would produce if it were made from coal or gasoline. Gasoline produces 46 MJ/kg. No common chemicals exceed that limit. As a practical matter, no device made of metal could even approach that, or one-tenth of that.
The highest energy density of a modern Li-ion battery is 100 - 265 Wh/kg. 265 Wh = 0.954 MJ (a suspiciously round number).
I guess if the active components of the LEC exceed that several times over we can be sure it is anomalous. I don't know what the active components would be. I guess we could just take the whole mass. I assume the 265 Wh/kg figure for Li-ion batteries includes the battery packaging and other inert components.