Exporting PNGs with Transparency Blending Modes

I've been trying to export this artwork in layers, where the red background is one PNG and the ornament design is another. However, when I export the image on a transparent background, there is a white circle around the shadow art (where I've used multiply), and a black line around the sparkle art (where I've used screen).

The left side is how it should look, but the right is how it exports. Any suggestions on how I can export the ornament as transparent PNG without the white and black effect? Is it because I've used the multiply/screen blending modes?