So, in English, the function a word plays in a sentence is described by the word order. Which is to say, “man bites dog” and “dog bites man” are completely different sentences. In Japanese, this is done instead by the particles (not participles – I’ve noticed you use that word in the past, too). Particles modify the word that comes immediately before them – they’re postpositions (as opposed to the prepositions we have in English). So long as you keep the same particles with the same words, you can rearrange the sentence however you like, and the meaning doesn’t change – word order doesn’t matter. Which is to say, 男が犬を噛む and 犬を男が噛む are the same sentence.

Honestly, you’ve pretty much hit the nail on the head – it basically IS like hard-wiring your brain all over again. Kids who are raised on English have completely different ways of thinking about language than kids who are raised on Japanese. You’ve also got the added disadvantage that when you learn your first language, you spent every waking hour of your first years learning it, whereas learning a second language now, you only learn when you specifically devote time to it. Basically, when you’re trying to think about Japanese, you need to try to stop thinking in terms of English.

I don’t know if I can suggest any books that will give you that magical “aha” moment, and I don’t know if I can provide it for you myself, but feel free to ask me any particular question you like, and I’ll give it a shot. =)