I’m familiar with the phenomenon, what I’m saying is “j” in pinyin represents a phoneme that we don’t actually use in English. Ironically, the “zh” sound in pinyin is probably a closer approximation to the “j” sound in “jiffy”. The hyperforeignism of Beijing seems to be from misapplying the reading rules for French, not Mandarin, so it’s an interesting case, but both pronunciations are only approximations.