This is somewhat unrelated with the above, but in the context of interesting information in relatively older papers by Holmlid et al, in dx.doi.org/10.1007/s10948-011-1371-6 (2012, paywalled) it is mentioned that a [static] magnetic field > 0.05T removes and prevents the formation of the ultra-dense phase of hydrogen (still called H(-1) at the time), converting it to higher energy states (regular Rydberg matter).
I thionk your point important - and perhaps closely related. I think we need to be very careful when discussing EM field effects on LENR since there is so much contradictory information (sometimes from the same source) on the topic. Since the prime source of an external magnetic field in most reactors is the heating element, perhaps we should consider the effect of this first.
Rossi, Parkhomov, and others have used various types of AC (single-phase/three-phase) as well as phase controllers and Triac/SCR systems for voltage control, there is a body of evidence to suggest that 'dirty' poly-phase current is no obstacle to LENR events. So it may be that 'ordinary' Rydberg Hydrogen is enough. I have certainly seen 'bumps' when using single phase AC with and without Triac voltage controllers, and when using DC, with and without PWM intervention in the heater circuit. I should point out here that as an equipment manufacturer as well as a researcher I have little wish to attempt to sell more stuff on the basis of such claims. Since the conditions are largely uncharacterised and I can offer no guarantees I don't make a few thermal bumps into a fanfare event. We are not talking about self sustain or 'heat after death' here.
But I must confess that with relatively low numbers of amp-turns in the solenoidal-form heaters I use (300A/t perhaps) the influence of the field on a fuel sample, even in the strongest magnetic zone is relatively tiny. I have also tried offering up 'Killer' Neodymium magnets to the system without seeing any effect. But that was a year or so back- i have learned better methods and improved my reactors since then.
So my conclusion is that 'the jury is out' on magnetism external to the reactor core- unless it is very powerful, because there is evidence to suggest that rapidly changing ANYTHING can stimulate and inhibit LENR reactions, though donning clean socks has not helped in my case.
Thank you for your inputs here btw, it really is much appreciated.