[Rhotchkiss]

I think Pete's analogies are pretty sound. There are some real T213 and Louisiana card experts on here, and maybe one or more of them will comment. Here is my take, I hope it helps:

T213-2 are not very rare; indeed they are fairly common. Perhaps Tolstoi, instead of American Beauty, in terms of scarcity. But on value, they sell as a common back T206 would.

T213-3 are rare, but can be found. You may have to spend some time and effort searching if you want a particular player combo, and you may have to be patient. Cost-wise, Type 3's are 2-3x more expensive that Type 2's, and are more in-line with the American Beauty, or perhaps Brown Hindu, analogy.

T213-3 overprint (pictured below)-- these are very rare, and I am not familiar with any where more than one example is known to exist (but I am sure there are a few). In terms if rarity, BL 460 is a solid analogy. I would perhaps go a bit further and liken it to a brown lenox or brown old mill. Value-wise, they are expensive but bring nowhere near a BL460 price; maybe like a black lenox (or a bit less)

T215-2 are rare. I think they are rarer than black lenox. I would say Uzit rare (relatively speaking), but with all the Drums and Uzits coming out lately, Uzits feels rarer than Drums and Drums feel as common as Lenox! Value-wise, these are probably about where the T213-3 overprints trade.

Two you forgot -- T214 & T215 Pirate backs (both pictured below). Neither can be considered T206's because they were issued in 1915 and 1912, respectively, and T206 is 1909-11. But they are well worth noting because, like T213-2/3 and T215-2, they have T206 front pics.

T214's are quite rare. Rarer than any other ones mentioned above except T213-3 overprint. These are tough to find. Value-wise, they sell for Lenox-Uzit prices

T215 Pirates are wicked rare (thats a technical term). There is one almost complete set known, and a smattering of others - maybe 20(ish) known. These cards are brown old mill rare, and they sell for brown lenox/brown old mill prices, if they even ever come up. Like brown old mills, all T213 Pirates are graded A (or should be) because they were not factory cut.