The problem I have with audio warnings is that if you don't use them sparingly, you'll have audio collision.
For instance, if all of your examples (or at least as many as would make sense to play at the same time) triggered at once, you'd either end up with the audio playing simultaneously, playing sequentially, or doing priority based filtering. The first (and optionally the last) of those options lose information, and the second (and optionally the last) means it's impossible for all the notifications to be timely.
Audio notifications need to be for things that either can't be trivially seen (missile lock and tone), or will result in almost immediate death if ignored (critical damage or surface collision warnings). You only really want one or two different types of notifications per context where possible.
Overshoot can be displayed trivially on the UI using a mixture of text, numbers, shapes and colour in the vicinity of the target.
Also, the autopilot could theoretically be used to prevent overshoot by slowing down for you. Sure that's easy-mode, but it's an option.