There is a single Double Die Reverse "
DDR"
Two Cent Piece and it is the 1866, but this is not one of them. You are correct on the MD and not Longacre's Doubling as well.
There are many Double Die Obverse "
DDO" coins in the
Two Cent series:
1864 Small Motto all Proofs and Business strikes are
DDO1864 Large Motto - 9 different DDOs
1865 Plain 5 - 6 different DDOs and 1 Proof
DDO1866 - 1
DDR 1867 - 3 DDOs and 1 Proof
DDO1868 - 1
DDO1869 - 1
DDO1870 - 1
DDO1871 - 4 DDOs
1872 - 1
DDOOnly the Fancy 5 and 1873 closed and open 3 Proofs don't have any known
DDO found.
That's 28 total double dies in the
Two Cent series, (that we know of so far). Most are pretty small spread and low interest but many are recognized by NGC/PCGS/ANACS for variety labels.
The 1866
DDR is a neat example here are some photos of what and where to look for it:


It does appear your coin has a slight "railroad rim" to it, where the coin is struck slightly out of collar, as well a small rim
Cud on the reverse around 11:00 - I like it as it's interesting and the die cracks make it more so IMO.
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