I like to play (The Settlers of) Catan on Board Game Arena with totally random number tokens. These tokens determine the production rate of the terrain tiles beneath:
There are 18 number tokens, two each of 3, 4, 5, 6, 8, 9, 10, 11 and one each of 2 and 12. A valid arrangement of these tokens on the board (19 hexes in a side-3 hexagon) has each token placed in exactly one hex, leaving one empty hex (the desert), and none of the 6 and 8 tokens adjacent. So a 6 cannot be adjacent to the other 6, an 8 cannot be adjacent to the other 8 and a 6 cannot be adjacent to an 8.
Task
Output a valid random arrangement of the number tokens. Each possible arrangement only needs a nonzero probability of being output.
You may output in any reasonable format, which may be 2D (like the valid and invalid outputs below) or 1D (e.g. mapping the hexes to a 19-character string in a fixed and consistent order). In either case it must be specified how the different positions in the output map to the hexagon. You may use any set of 11 different symbols to denote the number tokens or lack thereof.
This is code-golf; fewest bytes wins.
Valid outputs
These use A B C for 10 11 12 respectively and . for the empty desert hex.
6 3 8
2 4 5 A
5 9 . 6 9
A B 3 C
8 4 B
B 9 A
5 6 C 8
6 4 B 5 3
2 8 9 3
A . 4
B B C
3 3 A A
2 4 6 . 6
4 5 9 9
8 5 8
Invalid outputs
This one has three 5s and only one 4:
6 A 2
C 5 9 3
8 B 3 6 A
. 9 4 5
5 B 8
The two 6s are adjacent here:
5 2 4
3 8 B 4
9 B 3 5 8
A 6 9 C
. 6 A
A 6 and an 8 are adjacent here:
4 3 A
. 8 2 5
4 6 A 8 B
5 C 3 9
B 6 9