Sandwedge 74,
It all makes sense except for your 'across the board' comment. Each hole at your course should have a handicap number from 1 to 18. Generally the odd numbers are on the front 9 and the even numbers on the back. These are the relative difficulties of the holes in relation to the others. Your friend with 7 strokes would get his strokes on handicap holes 1 through 7 only. So it shouldn't be so bad for you not to be able to choose the holes as they are laid out to you by the course. Your friend only gets his strokes on the 7 hardest holes assuming an even distribution of difficulty between the front and back 9. Also remember that both your friends handicaps and yours are generally based on the best 10 scores out of your last 20, so shooting much better than their handicap should be a rarity. As they improve, it will get tougher for them if they are honest in submitting their scores and factor in ESC when submitting.
Have fun, and play some closest to the pins on the par 3s for beer. It always brings out the best in me and my playing partners.
Oh, and feel lucky, you'd be giving me close to 30 strokes over 18 holes. But I am improving and the handicap index is coming down.