Eric,
Where we differ is the idea that LENR is in an initial "non-scientific" mode.
There are two factors here:
(1) Your Pd-D vs Ni-H distinction
(2) Your contention that things are still non-scientific
Pd-D vs Ni-H is interesting. The two sets of phenomena are superficially similar, but in terms of any physical model of LENR very different. Of course, in terms of my preferred "error + chemical" model they are natural bedfellows and the phenomenological similarity comes from a causal similarity.
So if you hypothesise the physical version of LENR you have an immediate decision:
(1) Pd-D and Ni-H are both true examples of this
(2) Pd-D is a true example, Ni-H is "error+chemical"
(3) Pd-D is "error + chemical", Ni-H is true example
According to which you choose you have different issues to reconcile.
For your comment to make sense I guess you follow (1). But in that case the inherent implausibility goes up further because the physical phenomena in the two cases are very different, and comprise two different extraordinary mysteries.
As far as theoretical physics goes the "four irrationalist" arguments don't hold, and Feyerabend in particular is just wrong. (I have some sympathy with Popper who makes at least one good point, though does not understand it mathematically as is now possible). Specifically the history of physics has been a clearly ordered set of refinements in which each advance explains both a large range of phenomena, and old phenomena more accurately, with the previous theory seen as a decent approximation to the new and better one. I don't claim that all science is like this. Soft sciences, for example, are rather different.
polemic but nevertheless accurate at least as far as physics goes:
http://ontology.buffalo.edu/stove/500-600.htm
and, for a mathematics that in principle neutralises claims of irrationality (I'll address the issue of objective priors for hypotheses if you wish):
http://bayes.wustl.edu/etj/prob/book.pdf
Also, if you follow (1), Ni-H may be non-scientific (I'd put that rather stronger), but Pd-D is now a mature field of scientific investigation. Why are the current examples of it not clearly sharper than the old ones?