Q:

Standard of proof required to prevent dismissal of criminal charge before trial

In New Zealand, a judge may dismiss a criminal charge before trial if "the Judge is satisfied that, as a matter of law, a properly directed jury could not reasonably convict the defendant" (CPA s147(4)(c)).
That is, if a Crown prosecutor (e.g. the Police) files a charge and fails to present convincing evidence, the judge may dismiss the charge and the case will not proceed to trial. The same applies to private prosecutions with the extra obstacle that charges may not be even accepted for filing because of the evidence being "insufficient to justify a trial" as per CPA s26(3)(a). In this case the same test as with Crown prosecutions applies (Mitchell v Porirua District Court [2017] NZHC 1331 at [31]):

The two grounds for exercising the discretion under s 26(3) are
  analogous to dismissing a charge under s 147 of the Act and guidance
  can be taken from case law decided under that section.

To what standard does the evidence need to be convincing so that the judge is satisfied that a jury could "reasonably convict" the defendant? Can circumstantial/cumulative evidence be sufficient? One might immediately think of the almighty "beyond reasonable doubt" standard for criminal cases, but would this be necessary for justifying trials? If so, how could it be up to the judge alone to decide whether the standard is met if this is what trials exist for?
Real use-case scenario:
It is alleged that the defendant intentionally set his dog on a couple of pet animals, and/or recklessly let the dog attack them. One was killed, other seriously injured. The charges are under the Animal Welfare Act (s28 and s28A) and Dog Control Act (s57(2)).
Evidence:

A formal statement from a neighbour who:
a) From outside his house, saw the defendant and his vehicle near the pets (alive / non-injured);
b) Went into his house from where he soon heard an unusual noise;
c) Went out again and saw the defendant with a dog on the ground;
d) Saw the defendant put the dog in the vehicle and drive off;
e) Saw the killed and injured pets at the scene with injures looking like made by a dog.
Photos taken by myself soon after the incident, showing the dead pet with internal organs poking out of its ripped back, blood, some of the internal organs and external tissue on the ground.

Does this evidence meet the standard asked about above? (Note: this is not the main question; the main one is about the standard — in the bold above).
The charges were not accepted for filing with this "justification":

... the witnesses did not actually witness any attack .. They heard an
  unusual noise ... There is no other evidence that the dog caused the
  injures... While it may be suspicious that the dog caused the death or
  injures, there is no evidence it did so, nor any evidence to discount
  another cause of the injury or death ... Neither of the ...
  [witnesses]  ... saw the defendant doing anything other than being
  near the scene.

A:

To what standard does the evidence need to be convincing so that the judge is satisfied that a jury could “reasonably convict” the defendant?
The High Court expanded on the answer to this question in Mitchell, the decision you cited, at [32]:

[In R v Kim [2010] NZCA 106] the Court of Appeal discussed the meaning of “insufficient to justify a trial” in the context of sufficiency of evidence:

It is for the jury to determine whether the evidence is, or is not, sufficient to establish guilt. It is not for the Judge to predict what the jury will find. The test is whether the evidence, if accepted by the jury, is sufficient in law to prove the essential elements of the charge to the required standard. If so, the Judge should leave the case to the jury and not withdraw it on evidentiary grounds.

Can circumstantial/cumulative evidence be sufficient?
In 2015, Dr Chris Gallavin, Dean of Law at Canterbury University, wrote:

Circumstantial evidence is the bedrock of inferential reasoning. As advocates, we are well aware that a case is not “weak” by virtue of it being based upon circumstantial evidence alone (a common misconception). Circumstantial evidence will often form the base of a strong case, again, in both the criminal and civil jurisdiction alike.

Does this evidence meet the standard asked about above?
Unfortunately this question is not allowed, because the rules state:

Please don't ask questions seeking legal advice on a specific matter. These are off-topic for Law Stack Exchange. While users generally contribute answers in good faith, the answers are not legal advice, and contributors here are not your lawyer.

The test of “insufficient to justify a trial” is somewhat Delphic because it calls for an evaluative judgment. That judgment can only be formed by a court with relevant jurisdiction.

