[greyproof=RMCS vs. $n$] Seem to have $[Q]_\mathrm{res}$ that grows exponentially in cardinality in $n$. Here is sage code that plots these quivers:
Code used to find the restricted mutation classes (requires this version of sage):
Here is a table consisting of $n$ and the corresponding $[Q]_\mathrm{res}$ cardinalities.
| $n$ | $|[Q]_\mathrm{res}|$ |
|---|---|
| $5$ | $6$ |
| $6$ | $6$ |
| $7$ | $4$ |
| $8$ | $4$ |
| $9$ | $5$ |
| $10$ | $6$ |
| $11$ | $7$ |
| $12$ | $11$ |
| $13$ | $12$ |
| $14$ | $17$ |
| $15$ | $23$ |
| $16$ | $31$ |
| $17$ | $40$ |
| $18$ | $58$ |
| $19$ | $76$ |
| $20$ | $109$ |
| $21$ | $149$ |
| $22$ | $208$ |
| $23$ | $287$ |
| $24$ | $410$ |
| $25$ | $567$ |
| $26$ | $803$ |
| $27$ | $1128$ |
| $28$ | $1599$ |
| $29$ | $2249$ |
| $30$ | $3201$ |
[/greyproof]