It's not impossible to get medals on the SS, it just take a little time as the drop rates are fairly low, and within those low drop rates, say when a Forest will drop a medal, all the medals now have a chance to drop. Another thing, it seems that each valley has 2 medals it favors to drop at a higher rate.

You also have to hit lvl 7-10 valleys so you have to have some troops built up.

The one, and only one advantage to this is as your going for your 3rd city which comprises of Lion and Rose, the Rose are so elusive it seems, that by the time you've gotten 10 Rose medals, you'll have enough of all the other ones to shoot up a bunch of ranks. I spent a solid 2 weeks of medal farming going for my 8 remaining Rose and 4 Lion medals using spamming valleys doing the capture and release method. When I got my last Rose finally, i had enough of all the other medals to get Furstin in one shot. I went from 2 to 9 cities just like that.

I also started collecting my data along the way, I'll present it. I'm on SS5 btw:

Lvl 7 Swamp

Freedom Total 17 (1.311%)
Wisdom Total 4 (0.308%)
Courage Total 1 (0.077%)
Honor Total 3 (0.231%)
Nation Total 3 (0.231%)
Justice Total 6 (0.463%)
Rose Total 2 (0.154%)
Cross Total 8 (0.617%)
Lion Total 4 (0.308%)

Total Runs 1297
Total Medals 48
Drop Rate % 3.700848111

Lvl 8 Swamp

Freedom Total 11 (2.477%)
Wisdom Total 2 (0.45%)
Courage Total 1 (0.225%)
Honor Total 0 (0%)
Nation Total 2 (0.45%)
Justice Total 9 (2.027%)
Rose Total 0 (0%)
Cross Total 4 (0.901%)
Lion Total 1 (0.225%)

Total Runs 444
Total Medals 30
Drop Rate % 6.756756757

Lvl 8 Forest

Freedom Total 1 (0.279%)
Wisdom Total 0 (0%)
Courage Total 5 (1.393%)
Honor Total 11 (3.064%)
Nation Total 2 (0.557%)
Justice Total 1 (0.279%)
Rose Total 6 (1.671%)
Cross Total 0 (0%)
Lion Total 5 (1.393%)

Total Runs 359
Total Medals 31
Drop Rate % 8.635097493

Lvl 7 Grassland

Freedom Total 0 (0%)
Wisdom Total 0 (0%)
Courage Total 0 (0%)
Honor Total 3 (2.041%)
Nation Total 1 (0.68%)
Justice Total 1 (0.68%)
Rose Total 0 (0%)
Cross Total 0 (0%)
Lion Total 4 (2.721%)

Total Runs 147
Total Medals 9
Drop Rate % 6.12244898

Lvl 7 Desert

Freedom Total 0 (0%)
Wisdom Total 0 (0%)
Courage Total 0 (0%)
Honor Total 0 (0%)
Nation Total 0 (0%)
Justice Total 0 (0%)
Rose Total 0 (0%)
Cross Total 1 (1.587%)
Lion Total 2 (3.175%)

Total Runs 63
Total Medals 3
Drop Rate % 4.761904762