In the Ñoldorin dialect of Quenya, all z (voiced s) became trilled r, a process Tolkien called rhotacism (the standard linguistic term for a sound changing into r); it is generally called the “Quenya rhotacism” in literature about Quenya (as opposed to d > ð > r which generally isn’t given a special term). The sound change of z > r was established all the way back in the Early Quenya of the 1910s, but the exact nature of this sound change evolved over time.

Conceptual Development: According to the Qenya Phonology of the 1910s, the change of z > r was a factor in the development of intervocalic d, with d > đ [ð] > z > r (PE12/15-16, 24). In this early conceptual stage intervocalic s did not become z, and only final “s > z > -r (PE12/20)” although s > z > r did also occur before voiced consonants (PE12/19). It is not unusual to see Early Qenya words with -s- in its stem form but r in its uninflected form, both in the Qenya Lexicon and other documents from the 1910s and 20s:

• ᴱQ. ankar (ankas-) “ear” (QL/98).
• ᴱQ. fandor (fandos-) “monster” (QL/38).
• ᴱQ. kar (kas-) “head” (QL/45).
• ᴱQ. peler (peles-) “fence” (PE13/147).
• ᴱQ. solor (solos-) “surf” (QL/85).

Where final s did appear in Early Qenya, it was as the reduction of consonant clusters like ss. Note that the last three examples reappeared in The Etymologies of the 1930s:

• ᴹ√KAS > ᴹQ. kár (kas-) “head” (Ety/KAS).
• ᴹ√PEL(ES) > ᴹQ. peler “fenced field” (Ety/PEL(ES)).
• ᴹ✶solos > ᴹQ. solor “surf” (Ety/SOL).

However, this final -s > -r was not the only phonetic development in the 1930s. Tolkien gradually reversed himself, so that intervocalic s > z > r and final s survived in Quenya. The first indications of this trend appeared in Qenya noun declensions from the 1920s and early 1930s, where kas “head” was the uninflected form but inflected forms showed kar-, as in plurals kari/karin (PE14/69; PE16/112-3; PE21/22). The reappearance of kár in the mid-30s indicates Tolkien vacillated somewhat on this conceptual shift, but intervocalic s > z > r was the sound change he described in the Outline of Phonetic Development (OP1) from the 1940s:

s. Initially this remained unchanged. Medially in AQ and the earliest PQ it also remained unchanged, except in certain combinations discussed below. Later, but in the classical period it became voiced to [z] between vowels. This pronunciation as [z] remained the standard TQ pronunciation, serving as it did to distinguish early classical s, th after the development of th, þ > s (but never to z).

Note 1. In Lindarin z went on to r falling in with d, r. In TQ and later writings certain forms with r of Lindarin origin appear. This is especially the case with names. For example: Q Tindómirel “nightingale” (and name of Thingol’s daughter), N Tinnuviel from Eldarin *Tindōmi-ĕselde. Tindómirel (PQ Tindómisel) (OP1: PE19/33).

In the first draft of OP1, Tolkien attributed the final shift of z > r to Telerin and the pure Quenya form of Tinnuviel’s name was Tindómizil (PE19/33 notes #25-26). He then revised z > r to be a Lindarin [pre-Vanyarin] change as above, not in general Quenya usage (that is, not by the Noldor). The same remained true in the original draft of the Outline of Phonology (OP2) from the 1950s, where Tolkien attributed z > r to Vanyarin (PE19/73 note #26). But Tolkien reversed this so that z > r in the Ñoldorin dialect of Quenya and in Telerin:

This sound z was retained in Vanyarin, and so in their Tarquesta. In Noldorin & Telerin not long before the Exile z became first the same as the ř (derived from d) and later with that became merged with r. Some names and words showing this Vanyarin s/z were adopted in N. TQ before the Exile. Also owing to the prestige of the Vanyar the rhotacism was avoided throughout by some of the Noldor, especially those hostile to Feanor, but it was nonetheless a normal feature of Exilic TQ. Since z was not a sound used in Sindarin the pronunciation of z as s was often heard in Exilic TQ, especially among those that restored þ for the s-product of CE th. This mode was called “the Lisp of the Loremasters.” An example is furnished by AQ tindōmi-sel(dĕ) “nightingale” > Q tindómizel (Ñ tindómerel) = Sindarin tindúmhihel > Tinnúviel (OP2: PE19/73).

In this last scenario, [z] merged with [ɹ] (ř) as derived from [ð/d] (probably pre-Exile), and then [ɹ] became [r] (probably post-Exile). These edits was made in green ball point, indicating revisions made around 1970. However, there are references to this Ñoldorin-dialect sound change in a discussion of omentielmo vs. omentielvo, so this conceptual shift must at least predate the publication of the second edition of The Lord of the Rings:

In this respect EQ [Exilic Quenya] represented the recognition of sound-changes which had begun among the Noldor before the Exile and had already caused Noldorin Quenya to diverge from the language of the Vanyar. The principal of these were: 1. the change of both z (from s) and ř (from d) to r ... Of these the last stage in rhotacism, the change of z (< s) to r, was latest & probably belongs in the early Exilic (PE17/129).

Indeed, Vanyarin words with z (versus Ñoldorin words with r) appear in the Quendi and Eldar essay written in 1960. Tolkien also mentioned the sound change z > r in The Lord of the Rings Appendix E, where it must have referred to Exilic Quenya:

áre was originally áze, but when this z became merged with [tengwa] 21 [6], the sign was in Quenya used for the very frequent ss of that language, and the name esse was given to it (LotR/1123).

Thus the tengwa k (áze/áre), originally used for [z] as the voiced version of 8 [s] (double-bow typically indicates voicing in tengwar) ceased to be used for this sound after ř and z merged, being replaced with 6 (óre). This fits with the OP2 scenario described above. Since [ð] > [ɹ] first (probably in PQ), it follows that when [z] > [ɹ] (probably in early TQ) the tengwa 6 would be used for these new pronunciations and k abandoned (so it could later be repurposed for [ss]). The confusion in r-tengwar (6 vs. 7) was probably a late TQ phenomenon, after [ɹ] > [r]. This specific scenario for these tengwar came out of a Discord conversation with Shihali on 10-18-2019.

Despite the fact that this sound change occurred in Tarquesta [TQ], Tolkien almost never used z in Quenya spelling, with rare exceptions for explicitly Vanyarin words like ezel(la) “green” and Auzel, and occasional aberrant forms like Q. hríza “snow” (PE17/168) and ᴹQ. tyaze “like” (PE22/119). The letter z also appears in Tolkien’s Quenya translations of Catholic prayers where he may have been emulating an archaic style (VT43/8-9). Even in the 1930s where this was supposedly a “Lindarin” sound change, Tolkien used r as the ultimate result of s > z, and this remained true in the 1950s and 60s:

• ᴹ√PHAS > fazne > ᴹQ. farne “foliage” (Ety/PHAS).
• ᴹ✶thausā > ᴹQ. saura “foul, evil-smelling, putrid” (Ety/THUS).
• √olo-s > olozi > olori plural of Q. olos “dream” (UT/396).
• ✶-sjā > sya > zya > Q. -rya “3rd sg. possessive” (VT49/17).