That's the problem right there: I am so requiring theme-breaking and or motif-deviations for phoenix's paradigms (new life, regeneration, resurrection motifs) it's: the total opposite of Shiva but more Siren than Ifrit.
For statement sake: Bahamut would be total opposite Phoenix but more Odin than Shiva, maybe even cental or neutral.
There seems to be a character-based spatial reality to the terrestrial avatars thinking on it in relation to the celestial avatars.