Conversely, having done montage stuff myself (some of it in a professional capacity) you sometimes really do not have time or money to make more than you need, so you need to get it all in the can or go home fucked. There might not be any more than exists. I'd love to be wrong but I wouldn't be surprised.
I know what you're getting at, which was why I reckoned there wouldn't be a 'full' (3-4 minute) track. However RokTV is so tightly edited there must have been some bits of the prepared song/video that fell outside of the edit.
The line "he was grateful, I shot his pate full" is clearly from a verse that we don't get to hear the rest of. (The musical elements in the background are slightly different in that bit too, a glimpse of the fuller track.)
It wouldn't be too much of a task to reconstruct the Uzi Lover backing track from its component samples, though there wouldn't be much to be gained from doing that.
I do love Uzi Lover, although musically it is a little bit out-of-step for a 93/94 gangsta track. I suppose the primary focus was to make the track funny in its bastardisation of recognisable (slightly too commercial) samples.