Good visualization exercise using a real board! I saw this video posted on reddit:
https://www.youtube.com/watch?v=u0fQF8Ula5Q&feature=youtu.be
It gave me an idea to do this with some popular classic and romantic-era games:
1. Read out or be fed four moves at a time (i.e. 8 half-moves).
2. Visualize what the board will look like after that until you're absolutely sure you have it in your head.
3. Quickly move the pieces where they need to go. Maybe to avoid rote memorization of move order, play off the visualized position in your head. And you could move white pieces first, then black.
4. Continue with four move sets.
5. At some point you'll reach your mark you put in the list where you'll do another 4 moves and then you should prompt yourself to find the mate, just like they did in the video.
6. As you progress to new games, try 5 moves at a time, then 6 moves, etc. At some point perhaps your goal could be to pick out classical miniature games that had mate on the board (or that you know ended with resignation because mate-in-X moves), and visualize the ENTIRE game up to the point when mate was inevitable and ask yourself to write out the moves leading to mate.
Obviously, in step 5 I referenced a "mark" where you prompt yourself to "find mate-in-X" or "find the tactic to win material" so this requires some planning ahead so you'd have to find some classic games where mate or a good tactic was forced and/or played out.
Here's a start for some famous games to consider doing:
https://en.wikipedia.org/wiki/List_of_chess_games#cite_note-49
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