The problem can be mitigated slightly by using landscape rather than portrait mode on the hardware Kindle, and longer line settings in various Kindle apps. Higher average # of characters per line with these settings means two things.
Lower number of line breaks per book, therefore lower expected number of awkward ones.
Larger average number of spaces per line over which to spread the space needed for justification.
Again, this is a slight mitigation of the problem, it is far from anything that could be dignified by calling it a solution to the problem.
And, depending on your preferences, it may trade off one problem (high probability of awkward line breaks) for a worse one (unpleasantly long lines).
This is one of those problems with Kindle that is shocking to me but doesn't seem to bother many people. Kindle is an amazing device, particularly from a hardware perspective (resolution, battery life, built-in light) but it is uneven, suffering from what seem to be easy-to-fix problems like the justification butchery you mention. It seems like they got many of the hard things right and some of the easy things wrong. I particularly resent the beautiful full-page Kindle ads I see, for example, in the NY Times Book Review. It is probably not true, but I can't help thinking: if only they put the same kind of effort and visual acumen into the device's software that they put into the device's ads...