A drop shadow is never going to convey the type sitting on any surface. Not ever. Drop shadows inherently convey depth of field.
You need more of a cast shadow and Photoshop doesn't have a Layer Style for cast shadows. You have to create them yourself.
In addition, if the "chrome" is sitting on the texture, light would reflect off of the chrome causing the texture to be lit slightly around the characters.
This is just my hobbling something together. But in short 3 separate layers with varying effects and transformations to create some specific elements:
- A slight off-center glow around the figure to convey reflective lighting.
- A cast shadow to convey depth but not separation.


Note how the cast shadow is not even around the glyph. It's been transformed to be inconsistent and convey lighting direction.
This is rather quick and dirty just breaking apart the png in the question, then masking etc. to get pieces to work with. Then show the overall goal as I see it. This would absolutely need refinement before any production in most instances.
Layer style on the white layer...
The layer itself is set to "Normal" with 100% opacity and 0% fill. The 0% Fill allows the layer styles to show but not the actual pixels on the layer itself.

Bevel and Emboss set to Emboss to add shadows outside the glyph on the textured background.

Inner Shadow is used to add a slight darkening on the glyph itself to further convey a light direction.

Outer Glow is used to add a slight brightening to the area around the glyph. Note the extra Noise added to emphasize the texture.

Although it's a "Drop Shadow it's used to boost the reflective lighting on the texture. This isn't actually used as a "shadow". It's far more of a highlight on the texture.