Merge layers blending based on background BUT without keeping background.

Hello. I am using photoshop many years now and I never had to do the following and I was surprised that  I didn't know how to solve it. 

So I am having 3 layers, two graphics and one background. I want to merge blending of the first two graphics - based on the plain black background that I have BUT without having to keep the backround as I want to have a transparent image to put to any background that  Iwant. 

So my goal is the following image (without the black background you see) : 

But when merging the first two layers (map and circle that has color dodge) I have a color alteration in the circle which is not acceptable. 

I've read numerous solutions and nothing works. I tried converting to smart object the first layer .. then rasterize.. then merging.. nothing works. 

So any ideas?