I have nothing to add about the UV-printing technology But here's something about the mock-up.
Have your logo as black on transparent and put it as a separate layer onto a layer that has some believable version of the matte surface in non-uniform light. A photo of the real thing would be excellent. I had a darkened photo of grey painted door. A gradient can be used, too. Avoid full black and white, the brightness range should be max. 20% to 80%

Copy the logo to the layer mask of the matte surface. Copy it at first to the clipboard. After inserting the mask hold the Alt-key and click the mask icon to get the mask onscreen. The you can paste the black logo.
The logo layer is useful later as 50% grey. With the levels or curves tool adjust the black to 50% grey. Hide the 50% grey logo.

The glossy layer must be inserted below. Again a gradient can be used. It must be black to white and it preferably should be more complex than a single slope. Maybe better result can be achieved from a random photo that has more light at the same areas than the fake matte surface, An example:

After desaturating, blurring, inserting the contrast (=curves) and blurring again to remove the banding:

The glossy layer is inserted:

The edges of the logo easily vanish, if you change the shading to less agressive. It is prevented by giving to the 50% grey logo the blending mode = hard light and adding the edge boosting effect Layer > Layer Style > Bevel&Emboss. Note: The light comes upwards and the boosted edge is thin. Adjust the opacity of the edge boost layer smaller to keep the effect subtle.

The brightness of the gloss must be easily adjustable. Insert an adjustment layer for it. Here the midtones are lifted a little:

The gradients generally can be too clean to be believable. Its possible to add a little grain. Add a 50% grey layer with some grainy or other texture. Set the blending mode = hard light. The effect depth can be adjusted by the opacity.

Save the work, duplicate all layers, merge the duplicates, make a couple of copies, too. Now it's time to fit the result into something. You must add a background image and adjust the result to fit into it. You can
- distort the perspective
- add some thickness (=paint vertical edges)
- adjust the gloss light curves
- colorize with Image > Adjustments > Hue/Saturation > Colorize
- adjust the general light
You cannot do all this to the final form without the background image. The following is thus only a test example.

ADDENDUM: This job is impossible in low resolution. Have at least 2000 x 3000.