The American occupation is not the primary cause of E->J or J->E linguistic flow. There exist many transliterated words from English and other languages in the pre-war era (e.g. albrech, from German for "work", became arubaito, for part-time job). There are large numbers of English-origin words or coinages dating to before, during, and after the war, with measurable acceleration after the Period of Rapid Economic Growth.

Incidentally, my tiptoe-around-this-when-in-Japan-because-it-incenses-nationalists opinion as a linguist is that modern Japanese incorporates by reference large portions of English. "Happy" is, for example, a word in modern Japanese. Not the transliteration -- though that is a word, too -- but "happy", itself, written exactly like that. "Happy" is comprehensible to substantially all speakers of the language and appears in many document corpora so frequently that it cannot be excluded from the Japanese language by any rational criterion. There's another few thousand words which superficially resemble English in modern Japanese. (There are also, of course, minimally a few dozen Japanese loanwords in English.)