V = I * R
and
P = V * I
No mystery with these equations. Assuming resistance stays constant, an increase in voltage also increases current, and vice versa.
Now, if power stays constant, voltage and current are inversely related; as voltage goes up, the current goes down, and vice versa.
It is my understanding that as you increase the BEC output voltage, you also increase the power consumption at which the servos operate. That may explain why increasing the BEC output voltage may lead to issues.
While you're understanding of the equations is true, I think you need to look at things a little differently. Your first equation, yes as you increase current, voltage would go up, but how do you increase current, especially in this application? You are changing voltage, so you need to use a different variation of the formula, or plug in the voltage number you are using, and then solve for I or current. You will then see, as voltage goes up, your current goes down.
So as you increase BEC voltage, the current goes down. You can't change the current, you can only change the voltage, in this setup. Power consumption can be calculated, but for ease, just assume it stays the same.