Hmm.. I can't really tell from the lo-res link, but from your description it seems like you're doing everything correctly. I haven't been able to duplicate what you're describing.. I imported several (still) images and adjusted their durations (longer & shorter) by dragging their right edges; I was always able to play through the entire length of the project. This worked when there were transitions applied as well.
Are you sure the still images haven't been accidentally converted to movie clips (maybe by some effect applied, intentionally or unintentionally) -- the snap-back behavior you're describing sounds like what might happen when you try to extend the length of a movie clip beyond the actual end point of the file.
If the project isn't too far along, you might want to try deleting everything and re-importing the images, just to get a fresh start -- try the adjustments on the freshly imported files.
Of course, all the usual troubleshooting steps could be tried, especially restarting the computer, just to see if the behavior is the result of some computer gremlins ;-) You didn't mention the system/version you're working with -- my results were with the current version of iMovie & Mojave. In general, if you include that information with a troubleshooting post, it can sometimes help (like if there's a known bug with a certain version, for example)..
Btw, I've moved this thread to the iMovie subforum..