Using effects might be a good way to differentiate and transition the tracks without having two really loud tracks turn into a wall of noise.
Here’s an idea. Set the fader in the middle, with the volume on the new track turned all the way down. Then, start the filter on the track that’s playing to slowly strip out the base, while turning up the volume on the new track. When the volume on the new track is all the way up, the bass on the old track should be all the way down, and then you can mix into the new song without as much overlap.
Hope this helps.
Of course, the trusty “backspin” on the track you are mixing out of is another tried and true way of getting out of an awkward mix.