Chris,
You're talking about two different climbs here...steepest climb, and fastest climb. Without getting wrapped around the axle about needle deflections, put it in a place that means the most; your windscreen. When you take off, if a tower or big rock is in front of you and you can't go around it, then you want whatever climb will get you over it.
Steepest means you move toward the tower more slowly, while climbing as steeply as possible. This is Vx. It may take you longer to get over the tower, but it will also take you longer to get to the tower, and your only priority is clearing the tower. Vx is a good obstacle speed when climbing as steeply as possible is the most important thing in the world to you.
Fastest means you move toward the tower faster, while climbing faster. You'll get to the tower faster, and when you do, you won't be as high. In a given time period you'll climb faster which is why Vy is a good speed when you want to get to a higher altitude as soon as possible...it's just not necessarily the best speed to choose when you're trying to get over an obstacle that's right in front of you. You won't climb as high in as short a distance travelled forward, as you would at Vx.
Clear as mud.
Vx occurs at your minimum drag speed. Remember the charts showing parasite drag and induced drag? One speed exists for a given airplane configuration and air density (altitude) where induced drag will equal parasite drag, and that's your minimum drag speed. Vmd. It's also the point where you will be able to climb at the steepest angle, because climbing is based on excess thrust. You won't necessarily be able to climb the quickest...your rate of climb may not be the highest, because minimum drag doesn't necessarily represent the point on the drag curve where the biggest surplus of power exists over drag...all it does for you is represent the steepest angle you can climb.
One way to think about it is pointing your aircraft straight up. If you have an aircraft that weighs a thousand pounds, and you can produce a thousand pounds of thrust, in theory you'll float there all day long. Add two thousand pounds of thrust, and now you're going up, up, up. You have climb performance. Lower the nose a little bit, and now you're not only going up, but forward. Keep lowering it a little at a time, and you'll eventually mark a point where the aircraft climbs the greatest gain in altitude for the shortest distance forward...the steepest climb. This isn't straight up, for your airplane because you're going to hit a point as you climb when lift is helping you, drag is at a minimum, and you've found Vx.
This won't be the speed that will get you to altitude the fastest, however. When going straight up, with some unholy amount of thrust, yes, you would be steepest...but few aircrft have that capability, so we balance it with forward speed. Rather than using pure thrust to hold the airplane up, we use some lift, some thrust. The speed that produces minimum drag makes for the steepest practical climb in your aircraft, but at a higher speed you'll come across a point where you will achieve the highest rate of climb. Vy. At this point, you are producing slightly more parasite drag than you were at Vx, but you've also got more excess thrust and more lift...you're climbing faster.
Your question centers around why Vx and Vy come together. Think of Vx as an aerodynamic question; it's a function of drag. The minimum drag speed will vary with angle of attack, and as you climb higher and higher you need a higher and higher angle of attack, or a higher and higher airspeed, to produce the same lift.
Think of Vy as a function of power. As power available decreases with altitude, Vy also changes. Power decreases in a piston airplane as air density decreases and thus engine output decreases, and as propeller efficiency decreases as the air density drops (air gets thinner as you go up).
At the same time, you're flying at a higher and higher angle of attack. Eventually the place where minimum drag and excess thrust meet comes together and you've reached your absolute ceiling. At this point, you can't go faster, you can't go slower you can maintain altitude. You have no more excess power, you can only maintain altitude.