Listen, too. It doesn't always work but I've found that sometimes I can get in the general vicinity of the sweet spot by listening intently as I slowly rotate just the pick itself. Sometimes, I hear a little "click" and if I concentrate on that area, I succeed. As I said, it's not foolproof but just something else to try.
As you get further along, you'll have so many picks, you won't worry about losing 8 or 9 (but as you get better, you also won't lose as many). My current main has over 150 picks in her inventory, just from looting and opening chests.
And, as others have said, practice coming over from Fallout 3/NV probably helped, too

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