One possible solution (depending on the style) is to find a style at about twice the tempo, doubling the rate of chord changes. I think the latest version of BiaB supports this automatically with RealTracks, but I'm currently back a version so I can't verify this. I just do this in BiaB, export the track as a .WAV file, and put it together in Reaper. No doubt RB and PT support the same functionality.

If you're really adventuresome, you could export the file at a tempo where it doesn't give any artifacts, and try using some other software to time shift. Different algorithms might give different results. Audacity has a time shift algorithm, as does Reaper. And even the same algorithm is going to behave differently with different parameters.

If you do go that route, be sure to export your audio using a lossless format, such as .WAV. Unless you've got the "audiophile" version of the RealTracks, you're already introducing some artifacts. The pitch and time shifting that BiaB does is going to introduce some additional artifacts, and exporting to a lossy format like .MP3 is going to make things worse.

I doubt you'll end up with better results than what BiaB gives you, but it might be worth a shot. Now I'll have to give it a try...