In the Valian Year 1350, Dairon (better known as Daeron), the Minstrel and Loremaster of Doriath, reorganised the cirth and added new ones, making the extension of the cirth known as Certhas Daeron, used for inscribing names in Menegroth. The Dwarves working for Thingol liked them and adopted them, making them known also in the East, beyond the Blue Mountains.
The nature and the timeframe of the standardization however are obscure; some point the similarities between q et 1 with 1 and 8 as signs that Daeron was influenced by the Tengwar, therefore this mustn't had occurred before the return of the Noldor. Unlike the previous system, the reversal of the certh had a phonemic significance: reversed cirth were softer versions of their originals. This also gives us another information: perhaps lenited consonants must have started to occur in Sindarin around that time.
We know that at one time a sound of mh (soft m) was needed at some later time and the most appropriate solution was to revert the certh for m to indicate its softening, but it could not be reverted (presumably it was the certh 5); therefore m was given to 6 (which until then had a value unknown to us), and 5 got the value of hw.
The same process took place with r, l etc..
Maybe at that time, also the distinct cirth for semivowels and umlauts (sounds like w, y and œ), were employed.