To be honest, the screenshot doesn't look cluttered at all, it looks very neat and tidy.
There are a lot of ways to work in de dopesheet, and a lot of different view-options as well.
Working with a long animation and VO, it's sometimes more handy to have everything in one file rather then to split this up in different files. Especially when you have to edit the timings.
The organization of the dopesheet hierarchy depends on the hierarchy you have in the object manager. You can use 'automatic' mode, which show you all animated items, but you can also drag and drop an object from the object manager into the dopesheet. You'll only see the keyframes from that single object. If you want to drag more object into it, you can do this as wel.
You can drag individual keyframes, or drag over a set of keyframes and move them all at the same time. If you click on an object on the left side of the dopesheet, you select all keyframes from that object, which you can then reposition or edit further.
Lots of possibilities, and without having the actual file or 'briefing' of what needs to be changed, hard to say. You can always send me a PM and I can try to explain / make a screengrab if you like.