It's hard to make up for LENR's lack of existence with clever engineering. But even if LENR existed, how do you think it would get around the problem described? LENR would make heat, low grade heat.
LENR is hard to reproduce even for those who can reproduce, but at this point we can be sure that LENR is not a fantasy land. Multiple scientists in multiple institutions are able to reproduce the experiment sometimes, so this is the science.
IMHO, external factors are involved, e.g. cosmic rays, which generate muons[0], or radioactive elements or gases decaying, and LENR devices are just boosting them.