You bring up some good points, @AlaMoi.
I learned a lot about materials and pan thicknesses by reading this post:
The post is a little out of date (as there are some newer construction methods which are a little different, and also because I think some of the pans out there are using less material to save on costs) but only a little--and the science is pretty spot on. Honestly I hadn't even thought about some of the stuff in there (some of which you just adeptly also stated in your post).
BTW, I bow down to your natural gas proficiency 
I'm a bit of an odd duck here, because I think of cooking as applied physics and chemistry. Instead of writing down recipes, I make digital execution plans which rely on the stovetop doing a lot of work that a chef normally does, to get repeatable results. I use a scale to weigh ingredients even when I'm whipping up pancakes for breakfast. I've never learned to be a good human thermometer (which is like a third of normal training for a chef), relying instead on induction and pan/probe temperature control to do all of that for me. So you, my friend, get lots of kudos and points in my book for also being able to gauge all of that with your senses. Some would say those are the hallmarks of a true chef. I'm more of a scientist-cook.
I don't know if copper reacts differently on a gas stove than on induction because I haven't ever used copper on a gas stove. I do know that gas can deliver enormous amounts of heat. And I do know that the induction-compatible copper pans I bought transfer 1600-1700 watts of power almost instantaneously to the ingredients in my pan (even moreso with a higher-wattage induction burner), whereas other pans I tried could not. When I set my induction burner to keep the pan temperature at 100 C (212 F), I can "see" the coil pulsing on and off because the water boils faster and slower in rhythm with the induction coil at that temperature barrier. It's kind of wild. That right there was my "ah ha" moment with copper.
Based on the article posted above, thicker copper should in theory hold heat a little bit longer and it should provide an even more even heating surface.
For me, I'm mostly looking for responsive heat and precision. I want to be able to pour milk into a stew pan, press a button, and know that the milk will warm up to 82C to pasteurize and to denature the proteins, then drop back down to 42C before beeping at me so I can add the yogurt culture and cover the pot with a cheesecloth. And then it'll happily count down 24 hours while maintaining 38C to incubate my yogurt and beep at me again after a day to put the finished yogurt in the fridge--even if I'm nowhere near the kitchen. I know that people do that (or at least the first part) with other stoves, and they do it without copper pans. But boy, I love the convenience and I love the taste of consistent results
Regarding holding heat, you also make good points there regarding thickness etc. A thick aluminum pan can do great (even better than a thin copper pan) at providing even heat--and it can hold onto heat even better. For times when I want to hold heat, sear, etc. I turn to my Kuhn Rikon Duromatic saute and soup/stockpots. Those have high quality thick disc bases which I believe are aluminum and they do a pretty darn good job. They won't, however, let me turn on the stove and start cooking in 20 seconds and they're more fidgety when it comes to creating digital cooking programs (since they are not very responsive), but they have no copper in them and they excel at what they do. But unlike copper, I get very little joy out of using them (as useful as they are); maybe I'm just a sucker for pretty things, and for equipment that responds to me in real time.
afs
