Simple Tips
Immediately stop putting any pressure on the bobby pin as soon as it starts to stick. This will allow it to stick in multiple spots before it breaks.
Remembering where your last pick was when it broke is easier if you pay attention to where it is in relation to the little chips and marks around the outside edge of the lock before you start turning it.
Full Algorithm
As far as figuring out where to turn the knob, use a modified binary search algorithm. A binary search is the same algorithm children are taught in school when they learn how to use a dictionary. This one is a bit different, as we have to test a couple points and compare before going left or right.
In these instructions, "test the point" means to turn the lockpick there and see how far it goes.
Start with a point in the middle. This is the "center point". The left endpoint is the point rotated all the way to the left, the right endpoint is the point rotated all the way to the right. Test the center point and make sure you haven't lucked out and found the solution already.
Select left and right test points. The left test point should be midway between the center point and the left endpoint. Similarly, the right test point should be midway between the center point and the right endpoint.
Test each of the test points. One will turn further than the other. The target point is on this side of the center point.
Repeat steps 2 and 3, but with the more successful of the last two test points as your new center point. The old center point will become one of the new endpoints, as well as the previous endpoint on the same side of the old center point as the new center point.
The width of the section that will turn at all gets narrower as the locks become more difficult. As you attempt more locks you'll get a better feel for how wide each type of lock's sweet spot is.
This can inform your choice of test points, as you might not always want to choose points midway between the center point and the endpoints. This is especially true if the initial center point turns a little. In that situation, pick test points closer to the center. If the center point doesn't turn at all, pick points closer to the endpoints.
If one of your test points turns far enough, you might not even want to bother testing the other point, as you can be confident you're on the correct side already.
Occassionally, neither the center point nor either test point will turn at all. This complicates things. You'll simply have to try more test points until one of them turns at least a little. Once this happens, you can use this as your center point and the nearest spots you tried on either side of it as your endpoints.
Technical Notes on the Binary Search Modification
A normal binary search is done on a set of ordered elements, usually numbers. This search is also done on an ordered set of points, but when we're running the search we're unable to directly read the value to determine if it is greater than or less than the target value. Instead, we can only determine the distance (absolute value of the difference) between the test point value and the target point value. To be clear, I'm referring to how far the pick turns. When it turns a little, you're far away, when it turns a lot, you're close.
Since distance is undirected, we don't actually know whether to go left or right after the test. This means we check both left and right, then compare to determine on which subset of the set we recur. Because our center test point is not the target point (if it were we'd be done already), we know that when comparing two equidistant points on either side, one of them must be closer to the target than the other. This necessarily implies that the target point is to that side of the center point, although it doesn't tell us which side of the test point we need to check.
So we recur and repeat.
If you plan on walking around in power armor you might have a problem since you can't eat people while in power armor. So you would have to exit the power armor to eat and then reenter which can get very tedious.
As for companions, you can tell them to walk away so that you may enjoy your meal in secret and then go fetch them when you're done. In addition to dogmeat not caring that you are a cannibal you can also bring Hancock who also neutral, or even better bring Strong. Strong actually LIKES that you eat corpses:)
Best Answer
Corpses that are too heavy to drag with the physics button may be lightened through dismemberment. Based on this behavior, I would surmise that boosting your strength through Buffout and related drugs may also prove effective.