Interesting site! I'll be sure to use it in the future if I run into unfamiliar words :D
Yeah, I listen to the sentence here again and I hear the "r" this time. I think it's a bit of a confirmation bias when you have the sentence in front of you - that is, you know the word begins with r, and so you hear an r. But when I encountered this sentence first in the listening section, I didn't know what kind of word to expect..
I actually thought the word began with a "g". The best I could come up with was "goede", but I knew that's not a noun, so thought it might be a word I didn't know, called "goete" (apparently does exist, and means, roughly, "stuff"). I'd never have worked out: "route". Logical from the context, but just doesn't sound like it.
No, the current example voice is spot on, actually.
I know /ɛɪ/ is not pronounced like 'aye' or 'ay' (since there is no English equivalent), but it comes close. Then again, that might depend on the English dialect.
/ɛɪ/ sounds like 'I' or 'eye' (and I pronounce 'aye' almost the same.. ;) ).