Ashley,
Thanks for the link on the shader compositor, very interesting reading.
For now, what I have done is remove the pixelSize uniform from my shader and instead pass in similar values for the text object custom effect via user uniforms. I pass it '1.0/Text.width' for my own pixelSizeUser.x and '1.0/Text.height' for pixelSizeUser.y. This seems to work ok so far for iPhone mobile, safari and chrome on MacOS, with both high and low quality fullscreen and multiple resolutions. If the text box size changes, I must update the uniforms. Also if I spawn a Text object with the effect, I also must update the uniforms for the Text object spawned.
I understand your comment on the complexity, I see different behavior of the effect compositor on mobile and desktop with existing effects, so I see that adding more uniforms, etc. may be difficult.