Syriac Priority/Primacy

I've been frantically finishing off my master's thesis for the end of June (hence the absence of June posts). One of my footnotes mentions the theory that the Greek NT, rather than being composed in Greek, is the result of being translated from Syriac. What could be the basis for such a hypothesis?
A key argument for the book length article by Raphael Lataster, “Was the New Testament Really Written in Greek? A Concise Compendium of the Many Internal and External Evidences of Aramaic,” edition 1c, March 2006, http://www.aramaicpeshitta.com/ treats as “undeniable evidence” the point that the numerous Greek manuscript variants offer translation differences due to the polysemy of Peshitta words. Thus Peshitta words are treated as inherently polysemous as though they are responsible for producing (at least) two different Greek translation equivalents observable in Greek manuscripts.

But it is erroneous to assume that Greek words are not naturally as polysemous, or that Syriac terms are more ambiguous than their Greek counterparts. To use one of Lataster’s examples, certain Greek manuscripts have PULH whist others have thURA in Lk 13:24 which, for Lataster, indicates that both are attempts to translate the Syriac noun tar(o which can mean either ‘door’ or ‘gate.’ But this assumes that in Greek PULH only means ‘gate’ and thURA only means ‘door.’ BDAG, however, indicates that thURA means either ‘door,’ ‘doorway,’ ‘entrance,’ ‘gate,’ and that PULH likewise can mean either ‘gate’ or ‘door.’ Hence the key assumption for Lataster appears to be based on a mistaken notion that words in the translated ('target') language are inhernetly less flexible/more specific in meaning than corresponding words in the source language.