Thanks for your study of References to YHWH in ancient Hebrew documents, Doug. As in much else of what you write it shows a lot of research and you present your arguments clearly.
Doug Mason : To claim [that the personal name
of God written in ancient Hebrew characters appears abundantly in early
manuscripts of the Bible] requires justification with the use of statistical evidence.
I haven't come across a statistical analysis of the number of times the
tetragrammaton is presented in square characters, in Aramaic, in
palaeo-Hebrew, etc but even so I think the claim in the Awake! is true.
The tetragrammaton in palaeo-Hebrew occurs in six or seven biblical manuscripts recovered from four of the eleven Dead Sea caves. These are 4QExod_j, 4QLev_g, 11QLev_b,
4QDeut_k2, 4QIsa_c, and 3QLam. 1QPs_b is probably biblical (Ps.127:3) but it is very fragmentary so uncertain. In addition, 2QExod_b is probably a rewritten Bible manuscript and the composition of 3Q14 is unclear. The most developed use is noticeable in 4QIsa_c where all the divine names, as well as their prefixes and suffixes, are written in palaeo-Hebrew.
In addition to these there are fragments of twelve biblical manuscripts which are completely written in palaeo-Hebrew. These are 1QpaleoLev, 1QpaleoNum, 2QpaleoLev, 4QpaleoGen-Exod_l, 4QpaleoGen_m,
4QpaleoExod_m, 4QpaleoDeut_r, 4QpaleoDeut_s,
4QpaleoJob_c, 6QpaleoGen, 6QpaleoLev and 11QpaleoLev_a.
The tetragrammaton is also represented in palaeo-Hebrew in a number of Greek papyri. These include 8HevXIIgr, P.Oxy. 50.3522, P.Oxy. 7.1007, P.Vindob. Gr. 39777 and the Aquila fragments of Kings and Psalms.
I obtained much of this information from the monograph Scribal Practices and Approaches Reflected in the Texts Found in the Judean Desert, by Emanuel Tov, especially pp.238-248 on Writing in the paleo-Hebrew script and its background if you are interested in further details.