Why are the referred to texts not having Rei as a natural consequence of the 'fire regeneration'? The arguments presented so far show - I think - that the texts describe the same events as those which can be read about immediately before the start (with a Rei glyph) of the calendars for the year in G and K (and in a more complicated way also in E).

The question is too important to ignore. We begin by looking at B, where we first can argue that the referred to text segment is at the end of side b and therefore cannot initiate any calendar. The argument is faulty, though, because in the E calendar Rei appear in the very last period (24). However, not even in E is there any Rei following the discussed glyphs:

Eb6-4 seems to be the last in a 4-glyph group, maybe referring to 364-360, while the following 4 glyphs (Eb6-5--8) perhaps are related to Aa1-13--15 (where number 15 can be read as a 'twin' glyph):

On the other hand, Aa1-14 surely corresponds to Eb6-8, and the laconic text of Tahua therefore seems to have only 2 glyphs where E has 4. There is no good parallel to Eb6-1--4 before Aa1-13:

Aa1-9	Aa1-10	Aa1-11	Aa1-12

The left part of Aa1-15 maybe corresponds to Eb6-13 (and surrounding glyphs)?

Why should there be any Rei following the text in B? There is no Rei in A, and there is not any Rei in E beyond the parallel sequence of glyphs. There is a vae, though, at Bb12-26, a vae which resembles (the top line is straight and leaning forward) that in Aa1-15:

Bb12-13	Bb12-14	Bb12-15	Bb12-16	Bb12-17	Bb12-18
Bb12-19	Bb12-20	Bb12-21	Bb12-22	Bb12-23	Bb12-24
Bb12-25	Bb12-26	Bb12-27	Bb12-28	Bb12-29	Bb12-30
Bb12-31	Bb12-32	Bb12-33	Bb12-34	Bb12-35	Bb12-36
Bb12-37	Bb12-38	Bb12-39	Bb12-40	Bb12-41	Bb12-42
Bb12-43	Bb12-44	Bb12-45

The texts in M and N give us no help, the texts are too damaged. In R, though, there is a further thread to follow. There is a Rei not far before the discussed glyphs sequence:

Probably one glyph missing here.						Maybe three glyphs have been lost here.
	Ra5-101	Ra5-102	Ra5-103	Ra5-104	Ra5-105

Then follows:

...
	Ra5-201	Ra5-202
Ra5-203	Ra5-204	Ra5-205	Ra5-206	Ra5-207
Ra5-208	Ra5-209	Ra5-210	Ra5-211
Ra5-212	Ra5-213	Ra5-214	Ra5-215

Ra5-210 probably corresponds to Eb6-15, while Ra5-214 (reversed tapa mea) may be another way of illustrating what in Eb6-9 is done by a reversed ihe tau. Moreover, the left part of Ra5-212 (haati) presumably corresponds to the right part of Eb6-14:

Eb6-9	Eb6-10	Eb6-11	Eb6-12	Eb6-13	Eb6-14	Eb6-15
				Eb6-9 is a reversal of the more normally designed Eb6-16.
Eb6-16	Eb6-17	Eb6-18	Eb6-19

Ra5-213 and Ra5-215 maybe together correspond to the left part of Eb6-17.

Beyond Ra5-215 we arrive at 'a new beginning':

Ra5-216	Ra5-217	Ra5-218	Ra5-219	Ra5-220

We recognize the sequence, which was not included in the glyph dictionary because of the strange tara (Ra5-218):

Ca1-1		Ca1-2	Ca1-3	Ca1-4		Ca1-5	Ca1-6
						-
Ha1-1	Ha1-2	Ha1-3	Ha1-4	Ha1-5			Ha1-6	Ha1-7
						-
Pa1-1		Pa1-2	Pa1-3	Pa1-4			Pa1-5	Pa1-6
Ea9-25		Ea9-26	Ea9-27	Ea9-28	Ea9-29	Ea9-30	Ea9-31	Ea9-32

The discussed text in R probably, therefore, describes the end of the cycle in a way reminiscent of the end of the calendar in E. Further 'proof' is given by looking at the glyphs immediately before the discussed text:

Ra5-101	Ra5-102	Ra5-103	Ra5-104	Ra5-105
Maybe three glyphs have been lost here.
			Ra5-201	Ra5-202

In the parallel E text Eb6-4 probably corresponds to Ra5-105 and Eb6-8 to Ra5-202. Three missing glyphs may be similar to those covered by Eb6-5--7:

 

Here 7 glyphs in line b5 seem to refer to the end of the previous year.
				Eb6-1	Eb6-2	Eb6-3
Eb6-4	Eb6-5	Eb6-6	Eb6-7	Eb6-8

These comparisons between period 24 in the E calendar and the text in R have resulted - I think - in a plausibility for parallel texts (though somewhat differently documented on the two tablets). Both have Rei, but not beyond hua poporo.