They only made small date zinc cents in Denver. 1982 was a transitional year they switched from copper to zinc at the end of the year. There are less small dates than large dates. But in 1982 they made 17 billion cents. Most large dates, and most copper. 1 single copper 1982-D small date has been found. Left over copper planchet mixed in with all the zincs. There may be another out there, but it's pointless to actively look for it. Sorry for the discouragement, that's just the reality. Yes I weigh my 1982-D small dates, just in case. But you can also weigh ALL of the 1983 cents. They are all supposed to be zinc but a few coppers have surfaced. Later years also. There are more off metal 1983 and later years than the single famous 1982-D small date copper. Finding one of these out of billions and billions of coins is unlikely. One usually turns up one day, but the odds of you or I finding it, is MUCH higher than Powerball odds.
On subject of LMC variations, Meow managed to find a 2000 WAM a few months ago. How difficult do you think that is to find? It is the only WAM/CAM the Meow has ever found.
The proof set from 1982 is from San Francisco and the 1982-S cent is a large date copper. All of them. Mint sets, anything could be in there.
Well with the mint sets, they are nice coins, but they are business strikes. There's really no value there. You might get a nice uncirculated small date. But you will be over paying. You can go through rolls of cents, and there's still tons of 1982's out there because they made so many. This way you get to look at some for face value, plus you can always pop something else. A wheatie, or a coin in great condition. Sometimes with those sets the most valuable "coin" is the token that came from the mint. If they assembled those sets early in the year, most of them are going to be copper large dates.