The grid above shows the final layout of a domino game played with a standard $28$-tile (dominos $0-0$ to $6-6$). The first domino played, the $4-4$ double is given, and solvers must complete the remainder of the grid. The red-shaded space is where the last two dominos in the set would need to go -- but sadly, though they would complete the layout there is not enough space for both of them. Solvers must also identify these two missing dominoes. To help solvers a little, doubles are the only dominoes that can change the direction of the layout and are set with their centre against the new direction. Looking at the start piece, heading left or right is a new direction, while moving up or down is in conformity with the layout.
As always, two dominoes may only abut if their numbers match.
To further assist solvers, crossnumber-style clues are provided below. They are split into Up, Down, Left and Right and indicate which direction the solver must eventually enter them into the grid. For example, if the solver were to find that $4113$ was an up-domino then the $4$ is entered in a cell, then the solver must move up to enter $1$, up to enter $1$ and up once more to enter the $3$. No entry goes round corners. Left dominoes are entered by moving left (West, if North is directly up the page), and Right dominoes are entered by moving right (East).
Solvers must perform a transformation on all answers before entering them into the grid, but this will become obvious as the clues are solved.
Notation: Capital letters represent positive integers with no leading zeros. Lower-case letters indicate clues: $2$u means $2$up, i.e. clue number $2$ from the up column. $\#$ indicates concatenation: $4\#1 == 41$. Numbers in brackets give the length of the answer (digit count) before transformation and grid entry.
Clues:
$$ \begin{eqnarray} {} & \mbox{Up} & {} & {} & \mbox{Down} & {} & \\ 1. &\small \ (M \times N)\# (2u \times N) & (4) &\hspace{3cm} 1. &\small \frac{D}{O}+M &(2) &\\ 2. &\small (M \times O) - S & (2)&\hspace{3cm} 2. &\small \frac{M \times O}{N}& (2) &\\ 3. &\small \frac{D-S}{M} + N & (2)&\hspace{3cm} 3. &\small ((N^N)^N \times M)\# N & (4) &\\ 4. &\small O^N \times (2u-M) & (3)&\hspace{3cm} 4. &\small O \times M^N +M & (3) &\\ \\ {} & \mbox{Right} & {} & {} & \mbox{Left} & {} & \\ 1. &\small (3u) \# (D\times N^O) & (5) &\hspace{3cm} 1. &\small D+O &(3) &\\ 2. &\small (2d-S)\# N^O\# N^N & (4)&\hspace{3cm} 2. &\small (2u-M)\# \left((2u-M)\times \left(\frac{M}{O+N} + O\right)\right) & (4) &\\ 3. &\small N \# O \# O^N \# (O+N^N) & (4)&\hspace{3cm} 3. &\small (M+S)\times O & (2) &\\ 4. &\small \left(\frac{M}{N} \right)^N & (2)&\hspace{3cm} 4. &\small (2u-M)\# \left(D\times S \times \frac{M}{N}\right) & (5) &\\ \end{eqnarray} $$
No answer, before or after transformation, has leading zeroes, and division is always exact (there will never be $25/3$ for example, only $25/5$). Each capital letter represents a different positive integer.
Final note on tags: there's no cross-number tag so I've used cryptic-crosswords as numeric cryptic crosswords are traditionally like this.