Illustrator CS6: How to convert a mesh from (white- grayscale) to (white- alpha) ?

I just finished a bunch of graphics, using almost entirely gradient meshes at varying levels of transparency. I used "screen" for the transparency mode, and every mesh point is a grayscale color ranging from white (bright spots) to black. This combination achieved a "glowing effect;" the black and gray colors appear as transparency when my designs are shown against a colored shape.
However, when I removed the background colored shape, the black and gray gradient points, which originally appeared as varying levels of white transparency, now appear as grayscale pixels. I'm definitely a beginner to Illustrator, but it surprised me that the gradient/screen's black and gray colors appeared differently without a background.
Attached is a simple example: A gradient mesh shows up with transparency against a red background. But when the red background is removed, a black color appears. I would like to convert the varying levels of black/gray to varying levels of alpha, as they appear when shown against a red background
Is there some way to convert the red to alpha, or the grayscale pixels to varying levels of white / transparency, without needing to click every gradient mesh point?
Original effect on one background color. (this is the desired transparency effect, only I would like it to be the same without a static background color)
But when I slide the background color away, grayscale pixels replace the transparency. (I wanted to keep the transparency where grayscale pixels were in the gradient mesh screen)
Without a background color, any export to PNG will have black pixels, instead of transparent pixels. (I wanted transparent pixels here.)
I'm software designer, so the reason I want to remove the background while preserving the gradient transparency is so I will be able to dynamically insert different background colors at run time, and/or insert other images between the background color and the gradient. Yes, it's true I could generate every combination of colors, but in my case that would mean exporting 36 images from Adobe Illustrator, as opposed to exporting just 6 images. Packaging 36 images would also increase the space required by my compiled application.
Is there some way to keep the desired transparency effect, while exporting for use against any background color?

This is the best solution. It worked, and all my "glowing effects" are now working correctly with transparency.
However, this requires copying the background shape over and over again, as well as clicking on every mesh in the layers window. My project has something like 100 mesh objects. I really wish there was some faster way to do this, especially since the "screen" transparency option implies it is a software setting. (It is much faster than clicking every gradient point, though.)
Thank you for your help.

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