You’re welcome Mark!
Good to know that you teach photography, this might helps from time to time to explain things in a much easier way. I always think of photography as the base skill to know before one starts with 3D.
My photography education was mostly auto-didactically, until I joint for six years at the HdK (now University of the Arts, Berlin, founded in 1696), where (besides other things) I took six semester Photography and six semester Cinematography, and other film related stuff. But starting with my dark-chamber around four decades ago and now shooting RED Epic Dragon, showcases easily a constant update as well. It never stops and I love it.
So, I guess you have the Chrome-pot light set up as a teaching subject. The classic drill to have no place to hide the camera nor the light. Having said that, the cylinder around the bottles with texture projection Flat or as Camera projection will result in a kind of congruent refection of the texture where the texture is parallel to the surface and a distorted one on the opposite side. And if both sided (front and back) will have the texture to be reflected, than you have four reflection. Please explore it, but this is my prediction. IF it is not inside and the camera moves, it will look wrong, how much will be determined by the camera move. If that is all you want, create an equirectangluar of each Bottle Content and apply in into the Environment channel. Not in any way correct either, but perhaps more forgiving when it comes to camera movements, having tested it. Note that any outside reflection will have less only from the back refraction, and then twice, whereby the front has only zero refraction.
Anyway, please find below a file that I had prepared for the Compositing Tag questions. Please note that I have pushed the reflection to 400% to demo it, not suggested for realistic renderings. There are also three separators to showcase the interaction among the bottle or not (lower part).
Scene file
https://www.amazon.com/clouddrive/share/DFmrUORBff8PXjAJYIPmh8CXjvEbqkOtDWwF27cLWrz
ENJOY