Gee wiz guys, why make it so complicated....
Think of these V speeds as tools you can use as a pilot..
Vx: Your flying along, you look forward and see a big hill up ahead...Vx is the speed in which you take to gain the most altitude in a given distance...and yes it is the steepest climb angle...but it's about obstacle clearance....you only have some much distance to get over this thing...in a small plane this speed might be 60kts...
Vy is more about the relationship between forward speed and vertical speed....meaning if your goal for example is to get up to altitude the quickest...you use Vy...now Vy on this same little plane might be 70 kts...it's a quicker speed then Vx, because speed translates into time, time can translate to FPM...and when it comes to getting up to alt...Max FPM is what we are chasing....
Another way to look at Vx vs Vy...imagine your need to get out of a canyon and there is no way you just fly straight out of it, so you do a circling climb, effectively making no forward progress to your destination......you could use Vy under these circumstances as that will give you the lest amount of time to get up and over...
Vx is a trade off of FPM and forward distance traveled, trading it for a higher climb angle vs Vy...