Short answer: If you need transparency for web, don't use blending modes. Long answer: Set the layers back to Normal mode, create proper transparency based on creating a selection or using channel math. Even some crude copy&paste of the greyscale to a layer mask might work. Then adjust the overall transparency and tweak the contrast with adjustments.
Yes, I would never have done it this way, but I'm stuck with PSDs from an agency.
If I understand correctly, you now have layers similar to the following screenshot.
If so, hide all layers except the Multiply layer.
Cmd/Ctrl-click the Multiply layer's RGB thumbnail in Channels panel to get a luminance selection.
Press Shift+Cmd/Ctrl+i to invert the selection.
Add a black Solid Color layer; it will automatically be given a mask from the selection.
Here's the resulting Normal layer with the red gradient revealed below it.
good idea, i will try that