I agree, what is seen on the 1976 dollar is
Strike Doubling (MD) and Flat Field Doubling. The FFD is indeed the result of striking the coins twice. In an interview I had with Master Engraver Walter Ott, I learned that the PL dollars during this era were being double struck. He told me that the exact same quality coins that went into the Mint Sets of the time were the same as went into the so-called Specimen Sets. The only thing different was the packaging. I always chuckle when I see the coin removed from the packaging called PL and others Specimen. They are exactly the same. BTW, he told me this in reference to FFD I saw on a 1974 nickel dollar taken from a PL Set. I think you see both
Strike Doubling and FFD on the dime too. Hard to tell for sure based on the images but pretty sure.