How can you manage where/how sentences get cut off?

Did you try the H&J numbers I suggested? Hyphenation can be off; alignment doesn't have to be justified.

In which case, you can try switching paragraph composers. You can find this setting in the Justification dialog (Ctrl-Alt-Shift J). The "Adobe Single-Line Composer" would try to fit that "the" on the first line of your example paragraph, maybe. It's most likely set right now to "Adobe Paragraph Composer" which probably is looking at that "the" and thinking that, if it wrapped it up to the first line, the rag would be more uneven; "Safety" would wind up too far in. 

If you don't like the decisions made by the paragraph composers you're using, all you can do is what Mike and Abhishek have suggested: add no break, play with the Justification settings, maybe track it in by a few points if you're the kind of person who uses tracking to copyfit. But basically, those are your options - you select a composer, make decisions in your paragraph and character styles, and then maybe do a bit of  No Break application here and there when you are "riding the lines" to make sure that your layout doesn't have any composition problems. I do a lot of manual copyfitting, myself, but that is a point of personal preference.