From what I researched, it seemed that the bird was an eagle rather than a phoenix, and that Malcolm Allison took inspiration from Benfica's crest.
http://www.standard.co.uk/sport/football/facelift-for-crystal-palaces-benfica-eagle-7593041.html
I felt I couldn't really compare the historical rebrandings with recent ones, because it's very hard to know what the fan reaction was at the time.
Whilst the Latin motto was first introduced to the crest in 1938, I think the motto has existed since the club's formation.
http://myevertonnews.com/what-ever-happened-to-nil-satis-nisi-optimum/
Thanks for the information about Prince Rupert - it sounds interesting, I'll take a look at that!