It sucks to say this but I would choose another song to rap over/remix.
I had to make a similar decision a few years back. I was looking to add some verses to a popular R&B song so showcase my song writing abilities. I wanted to make it sound like I did a professional remix.... so I kept most of the singer's vocals like they do for real remixes.
I wanted to use one song.. but could only find the instrumental and not the acapella. So... I landed one Neyo's Sexy Love song... only b/c I found both. Turned out to be one of my best works to date... to the point where I forgot what song I was working on prior.
Moral: Don't stay stuck on this song if you can't find what you need. Move on and find another one... it might pay off.