Light mask overlay without lighting the sky

I'm using an overlay to create a lighting effect in a 2D game. The overlay is a grey-scale mesh and I multiply each pixel of the mesh with the pixel already written to the framebuffer.

This works great. The problem is that the mesh shouldn't draw over the background/sky because lighting shouldn't affect those. I have a few solutions for this but I keep thinking I'm missing something simpler.

Solution 1.

Draw everything except the background with camera 2

Render the overlay and make sure the shader doesn't alter the existing pixel's alpha values (so anywhere the background would show through has an alpha of 0)

Render camera 2 to a render texture

Add the render texture to a screen sized plane that sits in front of the background

Compose the background and the render texture using alpha blending

Solution 2.

Set the shaders for the background and overlay so that they don't write to the z buffer

Render the background

Set the shader for everything else to write a specific z buffer value, say 0.5

Render everything remaining except for the overlay

Set the overlay shader to only write to pixels if it's z value is greater than the zbuffer. Position it somewhere where it's z value will be greater than 0.5

Any other solutions that I'm not thinking of?