AHH!
I completely forgot about Freeverb! Haha I was using the standard Logic Pro reverbs and it was hard trying to get a satisfying result. I forgot I had Freeverb. Anyway, there isn't a pre-delay option on Freeverb3, but I got something very similar to what I was hoping for.
I also put in a better snare for the whole song and its much tighter with more bottom end around 250-300Hz. (I was pushing the limiter too hard on whole drumset, so consequently it smashed the snare, but somehow the rest of the drumset still sounded clear. So I made a seperate track for the snare completely uncompressed, and oddly enough it produced a pretty good result, no volume loss whatsoever and no clipping problems.)
A little more fiddling around and I'll post an updated clip.
Anyway, thanks for yalls help.