. . . Here are my opinions based on information currently to hand:
Günther Reinecke
I have looked at a copy of Reinecke's thesis . . . Reinecke does not evince the sort of casual or visceral anti-semitism found in the Taubner verdict. . . .
Authenticity of the Taubner verdict
I stress that this is only a theory - or desperate guess if you will. Nonetheless, I'm being serious. Two things would have to have happened for there to have been a miscarriage of justice in the 1961 investigations into Reinecke. Firstly, the Taubner verdict would have to been wrongly associated with him, or somehow misrepresented. We have still not seen his signature on it or an official stamp that would connect him with it. . . .
Work to do
It should be possible to get a copy of the original verdict. There is an essay on the investigation into Reinecke in HGS - this needs to be examined in detail.
In Büchler's article in HGS, we can read how Himmler directed that Täubner be tried in a higher SS court than the case warranted on its face and that
The head of the SS legal system, Günther Reinecke, was appointed head of the tribunal, and the investigating judge was Meurin, the prosecutor who had interrogated Täubner and his men.54 The proceedings against Täubner were, according to Himmler’s opinion of 26 October 1942, a secret “field trial.”
Büchler describes Himmler's interventions, which included directing which court to use for the case, guidelines to SS legal officials for handling of state secrets regarding killing of Jews (when such killings were prosecutable and when not - Bender, document of 26 October 1942), secrecy of the proceedings, importance of the photographs in the case, edits to and approval of the verdict, and handling of Täubner's appeal including probation. The case and verdict were carefully considered - not casually or viscerally - by senior officials within the SS; the verdict was the outcome of official deliberations and policy review, not the product of an individual's sensibilities as you try having it in a Reinecke fishing expedition of sorts.
Whilst I appreciate reflections on Reinecke, it's important to recall the context in which he worked, with what superiors and guidelines. In fact, Büchler writes about Brause - "The SS judge, Obersturmbannführer (Lieutenant Colonel) Dr. Brause, who wrote the verdict" - and cites testimony of Brause in this regard (VA, TR-10/752, p.9). I take it from this, although Büchler doesn't say so directly, that Brause authored the verdict, directed by Reinecke as the head of the tribunal but also overseen by the Reichsführer-SS himself. Poor, sad Reinecke is not being thrown to the wolves in this process, no matter how hard you speculate (it may interest you to know that Büchler finds Reinecke's postwar testimony particularly dishonest).
Büchler's citations are to the trial documents and verdict - Feldurteil 25 May 1943, YVA, TR-10/711. Büchler also quotes from testimonies about the actions conducted by Täubner's unit, testimonies you surely will not like reading ("original documents are in ZSt. Best II 204 AR-132/1, and the copies in YVA, TR- 10/1080, 101, 711, 752").
To make your speculations even interesting, you really need to review the materials in the archives cited by Büchler and at the very least contend with his article.