@Gobbledydook
About the country changes, if you use like the following permutation:
Players: 1,2,3,4,5,6,7
Game#1: A,E,F,G,I,R,T
Game#2: T,A,E,F,G,I,R
Game#3: R,T,A,E,F,G,I
Then the player 1, in the first game with Austria, will know the very same player with England is Austria in Game#2. Which is not good, because he can expect the same behaviour from that country. Of course everyone would know this, even though it's not really random.
What you have to do, is create sets of permutations, where every player gets 1 country, create like 5-10 of these variations, or even more, and let the moderator pick 1 set and assign the countries according to that. So no player will have any clue about his neighbour in game#1 who could be in game #2. Also games shouldn't be numbered, or at least the first row should assigned to the first game created.
For example, here are 2 sets, you should give to the moderator, and ask him/her to distribute the players according to in one of the sets below, so noone will have information, who is who in the other games.
Even better if the moderator can generate a set alone, so noone will have any info about which set you guys are actually playing.
Columns are the players, rows are the games. Rows should be varied in order not to match game creation order, or sets should be unpublished. Either way it's good.
Set 1
Game #1 R G E T A F I
Game #2 I F A R T E G
Game #3 G E T I R A F
Game #4 F A R G I T E
Game #5 E T I F G R A
Game #6 A R G E F I T
Game #7 T I F A E G R
Set 2
Game #1 A F G E R T I
Game #2 I T A R F G E
Game #3 G R T I E F A
Game #4 T E F A I R G
Game #5 F I R G A E T
Game #6 R A E T G I F
Game #7 E G I F T A R