I don't believe that this is a process broken into moving cards 1 at a time.
(excepting cards like improvisation, also the exact timing on crystal joy might be interesting.)
In the "Deed cards" and the "end of turn" sections it says.
Rules Quote wrote:
Deed Cards - At the end of the turn, all played Deed cards go to your discard pile. Unplayed cards remain in your hand, unless you decide to discard one or more of them.
End of Turn - b. Put all cards played this turn into your discard pile.
I read this to mean that they are not move in individually, but as a group.
Any other solution would also contain the complexity of which order do they go to the discard pile in? FIFO, FILO, or any order of my choice?
So I read the word "all" to mean they are moved as a stack.