Neutron production is a tell-tale sign of D-D fusion. The reaction itself has just under a 50% chance of producing a neutron every time two nuclei fuse, which is then easily detectable by specialized equipment. The other fusion products (protons, tritons, and He-3) are all ions, and are therefore nearly impossible to detect as they will be absorbed into the walls of the vacuum chamber with ease (and any detector inside the chamber would likely be overwhelmed by the X-rays and electron radiation produced by the high voltage source).
In addition, D-D fusion is well characterized - curves exist providing the reaction cross section for a wide range of energies. This empirically-gathered data gives a reasonable chance of fusion at the energies produced by accelerating ionized deuterium across the kinds of potential gaps provided by pyroelectric crystals. D-D reactions can be produced via all sorts of devices, from DIY fusors to deuterium discharge tubes to multi-million-dollar containment fusion facilities. The voltage produced by a pyroelectric can be observed to be very high, either by measurement in a vacuum (for insulation) or simply by observing the arcs produced.
No naturally occurring processes on Earth produce significant numbers of neutrons. Cosmic radiation produces a few, as do fleetingly unlikely nuclear decay processes from spontaneous fission. A quick look at the results of neutron detection schemes will show very low neutron flux from background. Turning on a fusor, pyroelectric fusion device, or other device capable of fusing deuterium will cause a spike in neutron production above background. Since D-D fusion already is known to produce neutrons, there is no reason to believe that the neutron count rate increase nearby the pyroelectric fusion device is not due to D-D fusion. The device is specifically tailored to allow deuterons to be electrostatically accelerated across a vacuum gap by the charge differential on the pyroelectric crystal. Destroying any of the necessary conditions for this (high vacuum to avoid premature collisions, deuterated target for fusion collisions, dilute deuterium gas, adequately sized crystal, proper crystal insulation) will cut short all fusion reactions and therefore neutron production.
There is no reason to believe that the neutron production encountered in operation of both fusors and this pyroelectric scheme is anything but deuterium fusion. Any unobserved, unproven additional nuclear reactions are not necessary to explain the neutron production since it is easily explained by the obvious: Fusion of deuterium.
You claim that these neutron producing reactions (that aren't D-D fusion) would produce mesons, but the lightest meson (the Pion) would produce muon radiation, which would be easily detectable as such (disregarding the fact that conservation of energy forbids the creation of said pion in the first place when smashing two deuterons together at ~100keV peak energy).
In short, I don't believe you. If you provide unequivocal proof of these reactions occurring, I'll change my mind. Because deuterium fusion is already proven to produce neutron radiation, by both professionals and amateurs. The simplest explanation holds.