I suspect it comes from "又做完了，又做得美丽," since that would make some sense. Is it something along these lines?
there's an earlier usage of "完美" in 唐 dynasty. in 漢文大藏經﹒毗尼作持續釋﹒卷五:
釋 若犯妄語。譬如大石破為二分終不可還合者。謂石大 完美 。四覩奇觀。比丘戒淨。人天欽仰。若犯妄語波羅夷法。不得還成比丘梵行。布薩羯磨不共眾僧。如石兩分。破壞本質。失眾敬瞻。棄置不盻故。
http://tripitaka.cbeta.org/mobile/index.php?index=X41n0730_005
so, i would suggest the etymology of "完美" is derived from "完整" + "美好"
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Sorry if this is obvious from your excerpt, but how do you know that the 完美 comes from "完整" + "美好"?– Hanry HuSep 5 '16 at 22:21
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1the metaphor of 犯妄語 is 大石破為二分 --> a big rock is broken into two halves. so 守戒 (not 犯妄語) is a whole, complete big rock. that, "完整" matched. next, "美好" is the most common term suitable for describing rock. anyway, it's just a suggestion for explaining 完美 in this buddhism text. have fun :)– 水巷孑蠻Sep 6 '16 at 1:26
完(adverbial - entirely / wholly) + 美(adjective - beautiful / excellent)
完美 is a compound word for "perfect, perfectly, perfection"
完 http://www.cantonese.sheik.co.uk/dictionary/characters/880/
|jyun4| jyutping
|wan2 | pinyin
[1] [v] complete; finish; bring to a conclusion
[2] whole
[3] [v] run out; use up
[4] a Chinese family name
美 http://www.cantonese.sheik.co.uk/dictionary/characters/257/
|mei5| jyutping
|mei3| pinyin
[1] beautiful; pretty; pleasing; fine; fair
[2] good; excellent; exquisite; nice
[3] be pleased with oneself
[4] [v] praise
完美 http://www.cantonese.sheik.co.uk/dictionary/words/9672/
|jyun4 mei5| jyutping
|wan2 mei3| pinyin
perfect, perfection, perfectly
宋 司马光 《太子太保庞公墓志铭》：“至於庐舍饮食，无不尽心为之驱处，使皆完美”。这是我索到的“完美”一词最早的出处。完在古代汉语可作形容词，意思是完整的，完好的，如完璧归赵。在司马光的文章中“完美”一词应是完备美好之意。至于完美一词什么时候变成现代汉语中“完美”(perfect)的意思，这个我就不清楚了。
to complete,sound and safe,to be ready,a reunion