Can you give reference as to where amA= first day of new moon. I have checked the dictionaries
Look up Apte (student dictionary)
amA... -f 1 The day of the new moon, the day of the conjunction of the sun and moon.
Hence
amA+Adi pUrNimA+anta tithy= starting from New Moon to Full Moon ending lunar days (tithy)
Your explanation
Also I think the waxing of the moon specifically alludes to her rising from mUlAdhAra to sahasrAra and becoming pUrNakalE.
is poetic and esoteric but how do we connect 'amA' with the mUlAdhAra?
(Darshan note the following too!)
akShara means undecaying/eternal. This is akaarantam pumlingam. The feminine (as it applies to dEvI) is formed as akSharA (TAp affix).
Hence akSharA is the eternal AdiparAshakti, whereas kShara denotes the ephemeral universe. Naturally akSharA +kShara = akSharakShara (samAhAradvandva)
Also according to Devi Bhagavtam Adi parAshakti is the creator of the whole universe including the Trinity.. She trifurcated to become, umA raMA and vANI and hence Shankar was correct!
It is not necessary for the whole lyric to be interpreted in the sambhOdhana. It is structured as:
hE bhagavti! tubhyaM namaH
Also note that kavi and kali are masculines declined like hari! They will remain the same (not become kavI or kalI when used to qualify women). The ikaarantam (hrisvam) are optionally declined like hari!