You can adjust the graph zoom to more easily select things. For example, hold alt and drag the right mouse button to the right to increase the horizontal space around the handles you want to box select, press space to deselect if needed, then hold shift and drag with the left mouse to box select the handles. If you use shift and drag with the middle mouse button then you don't need to deselect (middle mouse always does selection, never manipulation). Keep in mind you can turn off auto zoom be deactivating the Auto button.
However, selecting multiple handles and adjusting them all at once is not usually very useful. Moving the selected handles in your screenshot won't result in the same curve for those keys. The keys would need to have the same difference in values in order for moving all the handles the same relative amount to result in the same curves.
Have you tried these preset curve buttons?
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One of those may give you want you need in one click. If not, then you'll likely need to adjust the handles for each curve. This should not be hard, one mouse drag per curve, and it is only needed when the curves are important enough that you can't use the presets. I don't think you can get the results you want by selecting many handles and moving them all at once. It's true that was possible in the old graph because the unit for the handles' Y axis was "percentage of difference in value" but it produced poor curves, it was just difficult to see them.
