Is there any "Word of God" or solid references proving that Parasytes cannot reproduce? Throughout the series, the more scholar-inclined Parasytes (Reiko Tamura and Migi) state that the Parasytes cannot reproduce (and they do not know their own origin).

Is there any canon reference or proof that this is indeed true?
The fact that it was mentioned in the show means that it is canon reference. So in fact, no, parasytes cannot reproduce. At least technically so...
If you remember, Tamura Reiko did in fact reproduce via the human body and gave birth to human offspring. However, what about parasytes? Well, no, parasytes cannot reproduce, however, there isn't anything against them splitting into multiple organisms.
The below answer is contradictory to the show, see the answer below by Mindwin.

For example, Tamura Reiko can split into two separate parasytes. So let's consider that if a parasyte split into two separate parasytes and both latch onto two separate organisms, or parts of the same organism. Both would cultivate and grow from the nutrients, and both would have different experiences, and thus develop different personalities. In this sense, parasytes can multiply like cells via cell division and in the process creating successful offspring. Sources? None for this, it's hypothetical, however highly possible and an interesting concept.
What supports this idea though? Both the fact that Tamura Reiko split into two separate parasytes with two separate personalities, and the fact that the parasytes can indeed grow - as seen when a parasyte infects a human and takes over that human or part of that human's body.
The parasytes are made up of cells which is explained by Dr. Yui. In this sense, this supports my hypothesis since cells can perform cell division, which ultimately is a form of reproduction. So we can't necessarily rule out the fact that parasytes have the ability to divide.

In case you're wondering, reproduction is covered in episode 15. Tamura Reiko splitting into two happens in episode 17. Dr. Yui explains the neuron idea in episode 10.
Short Answer: No, parasytes cannot reproduce, and there is nothing that supports that they can reproduce via sex organs.