Have you read the article on annealing and orange peel in the LL? Vol 24.1 Issue 90 April 2014 starting page 23.
So I just re-read that article–an interesting read, one of the better LL has published. I think I get the gist of temperature on grain size as an explanation for “orange peel”. I actually wondered about this when I photographed the surfaces of your 1864 no-L, especially on the portrait–it shows up well in my pics. 😀
I’ve not found definitive proof that planchets were annealed at the mint – that would have been a massive operation. What is known is that the mint contracted the making of planchets to an outside contractor.
Yes, I’ve also read that planchet production was farmed out from the very beginning at the Philadelphia Mint. (And the first copper planchets were a disaster–poor quality metal that partly explains the condition of these coins today, as compared to contemporaries minted in the UK). The link below discusses a planchet annealing furnace at the SF mint. However, the situation might be totally different in the 19th C.