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.)
Cause, no, but definitely the turning point in the tide. Before and during the nationalist fervor of the war, there was a bit of a movement to purge Japanese of foreign loans (敵性語 "enemy language"), similar to sauerkraut turning into "liberty cabbage" etc in the US. Once the war ended, this was swiftly reversed and the floodgates to importing foreign terminology wholesale (re)opened.
China wasn't an "enemy", the Japanese had already conquered large swathes of it. The US and Britain were.
And yes, you can write "pure" yamatokotoba if you try hard enough (see eg. Shinto prayers), but the end result is as contrived as trying to write English without Latin, Greek or French loans.
Uncleftish Beholding (1989) is a short text written by Poul Anderson. It is written using almost exclusively words of Germanic origin, and was intended to illustrate what the English language might look like if it had not received its considerable number of loanwords from other languages, particularly Latin, Greek and French.
The Japanese loanwords in english that are not japanese cultural terms (like sushi, harakiri, etc.) or botanical (shiitake, kudzu) are few. The ones I can think of are: Honcho. Hunky-Dory (of apocryphally valid etymology). Kaizen. Tycoon. Tsunami. Bokeh. I'm glad that Karoshi hasn't made it into english yet.
I don't know if you got caught by autocorrect or something, but the German word for "work" is Arbeit. (Which would indeed transliterate into arubaito.)
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.)