How about instead of preventing players from switching countries for 12-hours after imediatley doing so, you prevent them from switching for only an hour AND not gaining perks during that hour?
The only con I can think of, and it's only one so far, is it may imediatley impede those who like to switch for an imediate improvement applied to the rate at which they gain perks. However, it should work twords their advantages in the long run, as I feel these are the players who suffer the most from the current 12-hour limitation. In less than an hour or two, they can find themselves on the largest side or one no larger or less than any other, and may feel trapped.
Another possibility is maybe in conjunction with the current 12-hour limitation, while removing it's "chain and shackles" from the game - if it's been at least 12-hours since your last country switch, then the 1-hour of no perks gained penalty will simpley not apply (thus, if you don't change "frequently", no penalty). A simple prompt when changing sides, warning players that it hasn't been 12-hours since their last country switch, would make it easily understandable in-game to players making the decision.