I was just flying rooks midwar - 21 Bish / 34 knits / 8 rooks
Early war previously - i had a perk mod of 12 ...only 4 on my side (knits)
I think the ENY / Perk modifier is the way to go, just crank it up to where it "hurts / helps" more. Maybe even double or triple the mutliplier..
An extreme example would be if one side side is WAY over populated...they might have 80% of the planes / vehicles disabled... Hell, if it gets so bad - have the entire planeset / vehicles disabled...
That would definetly get players to switch. Even if the most loyal of all chess-piece lovers couldn't fly...I'm sure they'd eventually switch.
On the other side..if the perk mod was rediculousy hi...the lowest numbered side, could actually be paid perks just for taking off in a plane

On a side note....If a country is pushing towards reset and is over populated... Make the reset perks correlated with perk / ENY.
So If you win a reset and are way over populated...you might only make 10 perks instead of the 75....extreme example - you win and you have 20 perks deducted from your total because of the outnumbering.
could be a fun experiment....