Seamlessly layering transparent sprites in OpenGL

I am working on an Android app, based on the LibGDX framework (Though I don't think that should affect this problem too much), and I am having trouble finding a way to get the results I want when drawing using transparent sprites. The problem is that the sprites visibly layer on top of each other where they overlap, similar to what is displayed in this image :

This is pretty unsightly for some of what I want to do, and even completely breaks other parts. What I would like them to do is merge together seamlessly, like so:

The only success I have had thus far is to draw the entire sequence of sprites on a separate texture at full opacity, and then draw that texture back with the desired opacity. I had this working moderately well, and I could likely make it work for most of what I need it to, but the large problem right now is that these things are dynamically drawn onto the screen, and the process of modifying a fairly large texture and sending it back are pretty taxing on mobile devices, and causes an unacceptable level of performance.

I've spent a good chunk of time looking for more ideal solutions, including experimenting with blend modes and coming up with quirky formulas that balanced out alpha and color values in ways to even things out, but nothing was particularly successful. My guess is that the only viable route for this is the previously mentioned way of creating a texture and applying the alpha difference to that, but I am unsure of the best way to make that work with lower powered mobile devices.

There might be a few other ways to do this: The most straight forward would be to attach a stencil buffer and draw circles to stencil first and then draw a full screen rect with desired color+alpha with the stencil, this should be much faster then some FBO with a separate texture.

Another thing might work is drawing those circles first with disabled blend and then your whole scene over it with inverted "blendFunc" but do note it might be impossible if other elements also need blending.

3rd instead of using stencil you could just use the alpha channel of your render buffer. Just use a color mask to draw only to alpha and draw the circles, then reenable RGB on color mask and draw the fullscreen rect using appropriate "blendFunc" also note here that if previous shapes have used blend you will need to clear the alpha to 1.0 before doing this (color mask to alpha only, disabled blend, draw full screen rect with color that has alpha set to 1.0)