The official translation is probably better, because apparently this creature is claiming to be a "perfect sage" himself. (But it depends on the story.)
Probably you're misunderstanding what この僕のように modifies. You're treating この僕のように as something like a sentence adverb, but this この僕のように actually only modifies the na-adjective right after it, 完ペキ. この僕のように完璧な仙人 forms a noun phrase that just means "sage who is as perfect as me" or "perfect sage like me".
If there were a comma after この僕のように, then it's possible to interpret it as a sentence adverb.
I can't speak English like him. = My English is not as good as his.
- 彼のように、私は英語を話せない。 (sounds a bit unnatural)
Just like him, I can't speak English (either).
EDIT: 仕様 here is not a synonym for 仕方（しかた, a way of doing） but a different word meaning "spec". As a suffix, ～仕様 means something like "-grade", "-spec", "-ready", etc (eg 冬仕様 = winter-grade). So strictly speaking, this sentence is talking not about actually becoming a sage but about the "readiness" to become a sage: "He could not be as 'perfect-sage-ready' as me ..." or "His body was not prepared for becoming a perfect sage ..." The official translation seems to have simplified this part.