And the puzzle colored in a way that actually works this time:
https://imgur.com/a/rRicHlD
And solved:
https://imgur.com/a/qCLmAL9
Break-in without first considering all options is this:
We know through earlier discussion that every value that is not in a center square is located in sets of 2x2 squares and are diagonally adjacent to one another. The cage shared by boxes 3 and 6 limit the positioning of where yellow and black can be placed in that configuration. Similarly, the cage shared by boxes 4 and 7 limit where purple and orange can be placed. The combination of those possibilities gives us this grid:
https://imgur.com/a/Nnbmn6t
The boxes connected in the green squares are three bi-value squares with an extra digit in a fourth square. Since we know that every non-center square is located diagonally adjacent to a square of the same value, we can eliminate not only the extra value from the square, but its matching value in its potential counterpart in the diagonal cell. That lets us place the orange in rows 2 and 3, the yellow in row 7 and 8, and in turn bumps out potential diagonals allowing us to place purple in rows 1 and 2, black in rows 8 and 9, and we're so far ahead of ourselves that we'll be able to place dark gray in rows 1 and 9 immediately.
And the whole puzzle whittles itself down with the same logic.