I have no idea why you would ever bother trying to do this in Illustrator. Surely you aren't supplying vector product mockups to clients. So I assume all you need is a jpg, png, or pdf of the mockup. Photoshop makes this very easy.... Illustrator doesn't. You, of course, want the vector (Illustrator) logo, but you can utilize that in Photoshop directly.
The first thing I'd do is get some blank product shots which don't have blown-out highlights. Good product photography will help immensely. The product shots you've posted will do nothing but make you work 500% harder for results that are, at best, 30% as good. Good photography makes a world of difference.
Then, for me, it would be a simple matter to set up a layer style I can apply to logos quickly.
I'd start with a straight black and white logo, no greyscale. Since it's being etched, I'm assuming black and white logos are used and preferable. So this shouldn't take any extra work.
Then I'd open the product shot in Photoshop and place the black and white logo as a smart object and apply a few layer options.
First I'd reduce the fill opacity for the logo to around 10% and set the layer blend mode to Multiply. This slightly darkens the area where the logo is present.
Then I'd add a small Bevel & Emboss layer style to add a bit of depth.
Note that it's merely a 1 pixel emboss. It's not much, just enough to convey a tiny amount of depth. The angle of the emboss should match the general lighting angle of the photo. The photos I used was shot head-on so 90° works best. The altitude of the emboss should match the general position (vertical) of the lighting. For the altitude, 90 equals dead front, straight on, lighting. Lighting from above will have a lower altitude number and lighting from below will have a higher altitude number. I set mine to 70° to indicate slightly higher than straight-on front lighting. Also note I've reduced the values for the highlight and shadows. These settings are more your preference as to what appears to be a good depth to you.
Depending upon placement and the product shot, you may want to 1) create a new smart object with your logo and the layer styles added by highlighting the layer in the Layers Panel and choosing
Convert To Smart Object from the Layer Panel Menu. You can then choose
Edit > Transform > Warp... and add a bit of a bulge the logo to mimic the curve of the product:
This may not be needed overall if the product shot doesn't have a sharp curve to it.
This is just a general method I'd use. A great deal depends upon the actual product shot but generally this type of technique will pick up (or rather allow to show through) the existing highlights and shadows of the object itself.
After all this, to change the logo, you just need to double-click the smart object for the existing logo, place a new logo inside the smart object, delete the old logo and save. Then close the Smart Object window and the product shot will update with all the appearance settings applied to the new logo smart object. So, once configured it should be very quick and simple to insert different logos.
If you must use Illustrator, the same basic technique would apply.... place logo above product, reduce opacity, set to multiply, then you'd add a small inset black stroke at a reduced opacity and a small inset white stroke at reduced opacity to indicate depth. You could use the Graphic Styles Panel in Illustrator to apply similar appearance settings to new logos down the road, provided you set up everything in the Appearance Panel rather than as separate objects.