I think I’ve got to dispute you on a few points.
First, Proto-Germanic is a proposed ancestor language to English, so it’s not right to say *twai was a loanword. It’d be like saying Modern English borrowed a load of words from Middle English, or Middle English from Old English. In reality the language just evolved.
Second, *twai is a reconstructed word, there’s no actual proof that it existed.
Third, Wiktionary seems ambivalent as to whether run came from Norse rinna or from Old English rinnan directly from Proto-Germanic, or a combination of the two.
Fourth, there’s a distinction between loanwords that have been in English long enough to mutate into entirely new words, loanwords that have stayed mostly the same but have received an anglicised spelling and / or pronunciation, and loanwords that have retained the original spelling and pronunciation (to a large extent.)
We’ve romanised the Japanese loanwords, OK, but the romanisation still reflects a Japanese orthography in hiragana. For instance, take hane; it reflects the hiragana は (“ha”) and ね (“ne”) and we pronounce it “ha-nay” in a way close to the original Japanese, rather than “hain”. If hane was an old loanword, like from the 17th century, then it would likely have been given an anglicised spelling like “hanay”.