However, it is difficult to imagine that such large ratios could be an error in calorimetry.
Let me amend that. It is impossible to imagine that such large ratios and such high absolute power can be an error. As Chris Tinsley said regarding the Fleischmann & Pons boil-off results, this is either real or these people are lying through their teeth. There is no middle ground. In the May 2008 experiment, input is 8 W and output is 3,400 W. Obviously you can conform that by holding your hand over the cell. There is no chance anyone would confuse 8 W with 3,400 W.
At least, there does not appear to be any middle ground. People have criticized the paper, saying the authors seem untrustworthy and they "come across as rank amateurs." I think the paper has too much theory and not enough actual detail about the calorimetry -- never mind the device itself. However, if it is real, it's real.
There have been many important discoveries in history that were poorly described and looked like amateur work, or like scams. Harrison's descriptions of his chronometer were hopelessly muddled, and that was one of reasons the device was delayed. (The main reason was political opposition from government scientists who were being paid a fortune to solve the problem by compiling lunar tables.)