remixing (specifically warping) songs/stems in ableton 8

[AQUEOUSI]

hey everybody! long time lurker, first post!

i'm trying my hand out at a remix (my first one) for the lastest beatport competition. play.beatport.com the song is "cowboy" by zeds dead.
i have been having an absolute NIGHTMARE warping the track to sit perfectly so i can start to chop it up/add in my own parts/etc. on beatport the track is listed as 88bpm, so unless i'm totally missing something i should be able to start a new set, set the tempo to 88 and line everything up perfectly to the grid, right? not the case. the best i've been able to do with this approach is using 87.5 as the bpm, which gets a lot closer but is still very slightly off. i watched a whole bunch of youtube videos on warping and intended on using the master/slave warping to warp consistently across all the stems, but due to the nature of the song and stems (there isn't a solid kick or anything going during the first or last vocal parts) i can't really get this approach to work seamlessly. does anybody have any suggestions?