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Instead, we should move on in the text:

Ka1-1 Ka1-2 Ka1-3 Ka1-4
Ka1-5 Ka1-6 Ka1-7 Ka1-8 Ka1-9 Ka1-10
Ka1-11 Ka1-12
... ...
*Ka1-17 *Ka1-18 *Ka1-20

When I once counted the glyphs I relied on Barthel's description of the K text in order to arrive at the 4 respectively 1 empty glyph places. Perhaps there never were any glyphs in these 5 empty positions. The Milky Way could have been in the way. If we count only the visible glyphs the numbers will lead up to 181 instead of 192:

Number of glyphs on the K tablet:
side a side b
a1 19 *5 24 24 b1 20 *2 22 119
a2 22 - 22 46 b2 17 *1 18 137
a3 21 - 21 67 b3 16 - 16 153
a4 16 - 16 83 b4 19 - 19 172
a5 14 - 14 97 b5 17 *3 20 192
sum 92 *5 97 sum 89 *6 95
Numbers with asterisk (*) refer to possible glyph positions where no glyph is visible.

Perhaps the idea was to have the visible glyphs reflect the number of days from Aldebaran to Antares:

Winter:  Summer:
180 183
Ga1-4 (*68) Ga7-16 (*249)
Aldebaran (68.2)  180.9 Antares (249.1) 184.35
'May 28 (148)  180  'November 25 (329) 183
Ka1-1 Ka1-2 Ka1-3 Ka1-4 Ka1-5 Ka1-6
Aldebaran (68.2) Theemin (68.5)        
Ka1-7 Ka1-8 Ka1-9 Ka1-10
Hassaleh (73.6) Almaaz (74.7), Haedus I (74.8) Haedus II (75.9), ε Leporis (76.0), Cursa (76.4) λ Eridani (76.7)
Ka1-11 Ka1-12
μ Leporis (77.6), ĸ Leporis (78.0), Rigel (78.1), Capella (78.4)  
... ...
*Ka1-17 (13) *Ka1-18 (14) *Ka1-20 (15)
λ Leporis (79.6) Bellatrix, Saif al Jabbar (80.7), Elnath (80.9) Nihal (81.7), Mintaka (82.4)
*Ka1-21 (16) *Ka1-22 (17) *Ka1-23 (18) *Ka1-24 (19)
 ε Columbae (82.6), Arneb (83.0), Heka (83.2) Hatysa (83.5), Alnilam (83.7), Heavenly Gate (84.0) Alnitak, Phakt (Phaet)  (84.7) γ Leporis (85.9)

Although the ordinal number for the last glyph in the line, 24, seems to suit the end of a line which could refer to the June solstice.

181 is also the number for the last day in June, where G has Sirius rising heliacally:

Ga2-5 (36) Ga2-6 (*100) Ga2-7 Ga2-8
ν Puppis (99.2), ψ3 Aurigae (99.4) ψ2 Aurigae (99.5) ψ4 Aurigae (100.5), Mebsuta (100.7),  Sirius (101.2), ψ5 Aurigae (101.4) ψ6 Aurigae (101.7),  τ Puppis (102.2), ψ7 Aurigae (102.4) 
'June 28 '29 '30 (181) 'July 1
Al Tuwaibe' 3 4 5 (45)  6

In other words, the K text could correspond to the time from January 1 to July 1.

Moreover, the message in the first 3 glyphs could be precisely this:

Only the top half - Ç - of the year is (in the text).
Ka1-1 Ka1-2 Ka1-3