Whereas you had stated:
Most The NWT translates John 1:1 as "... and the Word was a god," not "...and the Word was God."
The reason they give is that the word theos doesn't have the definite article in front of it in the Greek.
In his 1982 book, "The Jehovah's Witness' New Testament," Greek scholar Robert Countess looked up all such occurrences in the NT (theos without the definite article) and checked the NWT.
He discovered that the WTS only followed their stated rule 6% of the time.
94% of the time, they translated it "God" anyway!
This is actually not true. As can be witnessed above, many who take issue with Jehovah's Witnesses' "New World Translation" of 'theos' in John 1:1c (as, "a god") often miss the point that the reason for translating this clause the way they do is because this is 'a singular anarthrous predicate noun *preceding the verb* and subject noun (stated or implied)' - that is, not just that use of the noun 'theos' in the third clause lacks the Greek definite article. (In the Greek language of this period, there was no such thing as an indefinite article; therefore, depending upon the grammar, syntax as well as the imediate, global and cultural context of the phrase, when translating to English, the decision on whether to add an indefinite article or not would be decided by the translator.)
Now, with regard to some specific examples of Biblical verses which do represent the same, basic, Greek grammatical construction of John 1:1c, please examine the following within your own prefered translation of the Bible and see whether the translators had, themselves, appreciated the need to insert either an "a" or "an" there. At each of the cases below, it has been found that most Bibles consistantly do:
Mark 6:49; Mark 11:32; John 4:19; John 6:70; John 8:44a; John 8:44b; John 9:17; John 10:1; John 10:13; John 10:33; John 12:6
As can be easily seen, at each of the above verses, identity of the one being discussed was not at issue; no, but rather, the class of the individual is. Following this same syntactatical pattern as that found within John 1:1c, it should be easy to appreciate how that Jesus ("the Word") can also be properly identified as "a god," but certainly not as "God," the one of whom he was just said to be "with" (1:1b).