I think there are few who have taken the time to do a cursory investigation of the subject who would have the slightest objection to the claim that Nature and Science have editorial biases against studies on the subject, even those individuals who believe that the work that has been done is complete nonsense. The claim is simply not a controversial one.
I don't think it would be a problem if you didn't waste your time reading non-peer-reviewed papers on LENR. The field will no doubt move forward without you (or not move forward, if it's bunk).
What is fascinating to me about this exchange, in an anthropological sense, as one observing experimentalists (perhaps you're one), is that I'm not even convinced myself that the LENR stuff is real. I'm simply intrigued by the possibility that those folks might be onto something, and there are no ties to academia or fears for my reputation to dissuade me from investigating the truth of the matter. Similar resistance was shown in the scientific community to the advent of the telescope, to the invention of the airplane, and, apropos enough, to the possibility of nuclear fission. That there were fads relating to polywater and so on does nothing to detract from this.