The translator's version is grammatically correct, but seems rather awkward in that it puts so many words between Ebooks and Papier, seeing as those are the things that are being compared here. Also, the translator version substitutes the specific meaning "environmental(ly) friendly* for the rather meaningless "better"/besser. But Carsten S's comment is correct in that the verb must come right after the adverbial phrase if that's how you're starting the sentence. There is, in fact, only one clause here; Meiner Meinung nach and trotzdem are just adverbial phrases, not subclauses, since they don't contain verbs. I think either one could reasonably placed in the first position depending on what you're trying to emphasize, but putting Meiner Meinung nach first helps keep the rest of the elements connected. So I think
Meiner Meinung nach sind E-Books trotzdem umweltfreundlicher als Papier.
is probably the best version.
Side note: It seems unusual to see the preposition nach after the phrase it's connected to, technically making it a postposition. Apparently it's allowed in the sense "according to", but not in any of its other senses.