Having recently encountered this issue, I searched the web for a solution and stumbled upon this thread, which to my surprise was not only left unanswered, but also seemed to be the only search result that was directly relevant to my problem.  Luckily, I was able to adapt some advice from a similar situation.  Since I finally discovered a solid method, I figured I would offer my knowledge to anyone else treading the same path as me.

I guess they call something like this a "wobbly" keyframe.   In After Effects, someone gave the advice to right click and change the temporal interpolation to LINEAR.  In premiere, I noticed that they were ALREADY linear, but then I recalled Shooternz post about a spatial ease.

• Highlight ALL the keyframes, right click, then select Spatial Interpolation and click on Linear.  This should solve the issue.  You can then add eases and such to meet your goals.

I knew from the beginning that it must have been an invisible knot in the bezier curves.  I pulled the bars in every direction, but all it did was tighten or loosen the knot, causing the motion to speed up or slow down, but it would always hit the knot and reverse before continuing forward. You know how Illustrator will create crazy-looking lines when you try to add too many points with strong curves?  Well the same logic applies to this, but Premiere has a much more difficult interface when dealing with bezier curves.  In other words, by getting rid of the extra curves instead of trying to fix them like you can in Illustrator, it fixes the problem much more easily.

I hope I helped to clarify the issue and help you understand the logic of what went wrong, so you can move on now and perhaps adapt this knowledge to future obstacles.