why can't the electrons get between two nuclei and cancel their repulsion (rather like muons can do)?
The problem is that the conduction electrons are spread out so they can't clump together in the space between the nuclei. This is due to the low mass of the electron. A muon is very much like an electron but is over 3,000 times more massive; this means it is 3,000 times "smaller" and thus can fit into the small space between the nuclei just fine.
The problem is not that the electron wave function can't get close to the nuclei. The problem is that the electron wave function can't get clumped together into a large enough peak to counteract the Coulomb repulsion of the nuclei. One way to see this is with the Heisenberg uncertainty principle. Since a muon is 3,000 times more massive than an electron, it has 3,000 times more momentum for the same motion. This extra momentum allows it to be more localized without violating Heisenberg.
One of the best physicist of the 20th century, Julian Schwinger, investigated cold fusion and felt that the physics community as a whole was closed minded about it. I *think* his idea was there was some sort of collective phenomenon (getting the palladium just right) that accounts for cold fusion. It can't be as simple as simple screening by conduction electrons. TBH, I think Schwinger was past his prime and was grasping for things he could apply his formidable intellect to that would be useful for humanity.
I believe the reason most physicists have a problem with cold fusion is the lack compelling experimental evidence combined with the lack of any satisfactory theoretical explanation. Remember that almost all of the interest in cold fusion was sparked by the totally discredit experiments by Pons and Fleischmann. The experiments could not be replicated and in new experiments there was no indication of nuclear activity.