Whether you use a glove or a tab, whether you hold the string on your fingertips, in the first joint, or between the first and second joint, are all a matter of personal preference. Try all of them and see what you like best.
The chances are that you are torqueing the string, which is making the arrow fall off the rest. This happens when you exert a twisting force with your string fingers, such that you are putting a slight "S" bend in the string when you draw the bow. All the force in drawing the bow should be in line with the arrow, directly backwards with your string hand and directly forwards with your bow hand. You accomplish this, as was mentioned, by keeping your string hand completely relaxed, so that it follows whatever angle you hold the bow at. You keep your string hand relaxed by using your back muscles to draw the bow, not your arm muscles. Your string hand should feel like it is a link in a chain, and you should feel it stretch out as you draw the bow.
You mention that "I think I was trying to curl my fingers around the string more as the weight started piling on, rotating the string/arrow off the shelf." You probably are right, and the back of your string hand was probably cupped; it should be flat. In fact, when you draw the bow correctly, the opposite of what you state should be happening: if the string rotates at all, it should be rotating into the nock, forcing the arrow against the shelf, not off of it.