I'm bringing this subject up to the top from the All-Clad digression of a week or so ago.
Dennison, you mentioned that the retinning place formerly on 26th St. was no longer around. I think you might have been referring to Retinning and Copper Repair; they've moved out to Newark. A link to their website is included below. They did a stunning job of retinning a small saucepan of mine (I shipped it to them); it took nearly 6 months, but I think that's about normal since there are so few people doing it anymore.
On the subject of thickness: I have a set of 5 tin-lined copper saucepans that I found at what was essentially a hardware store in Bayonne, France. Looked like the pans had been gathering dust for a while, but I got the whole set, including a lid for the largest (8") for 1300 FF (@ $225 at the time). They're home-cook grade, meaning the copper is @ 1.5mm, but very well made (I don't have access to them right now, or I'd pass on the name of the manufacturer). I've never had a problem with hot spots, but they do heat up VERY fast & I use much lower heat than with other cookware. I don't use them for everyday cooking, usually just sauces and confectionery.
Which leads me to reiterate a point that gets made here over and over -- there's no one kind of cookware that's going to perform well for every task. IMO, investing in copper for everyday is a waste of money. If you want to get into copper, start small -- maybe a 10" sauté pan and/or a smallish (5") saucepan. I have more cookware than you can shake a stick at -- including lots of copper, Le Creuset and All-Clad (Master Chef) -- and the pans I use the most are a $10 non-stick omelette pan from K-Mart, a #10 Griswold that I got for $1 at a tag sale and a 3 1/2 qt. A-C lidded saucepan.