Hey, the idea sounds good. I just fell in love with the switch side idea.
First Idea: I agree, tanks and choppers are a bad ideas... at lest at the beginning. I think as the game progresses, the 2 major nations will supply them slowly because they have other priorities.
Related Idea: I think the "other" nations should be in a neutral state, but if you do something really good, like activate the best ending for a mission, a nation might give you some weapons... ex: If there is a mission you protect a convoy and not one unit is destroyed, Japan will give you some weapons. It wouldn't always be Japan.
Second Idea: Making you change teams is not the easiest idea to tackle. You could make a mission that you are sent on a special mission and you get in a trap and are surrounded. They give there point of view and you have a choice to choose your side. If you join them, they don't kill you, if you say no, some Bradleys conveniently come and save the day.
Third Idea: If the second idea is too hard to do, we could make the campaign from 2 prospectives on opposite sides. First maybe the USSR supported side looks like the bad guys, but later on the player can interpret any side being the "good guys" because the U.S. backed side could be really corrupt.
Forth Idea: Each "main" nation sends in some special forces... playable?... up to you. Use addon special forces for each side, I can give you some addon recommendations if you like the idea of special forces.
Summing it all up: I guess that was it... I think I am forgetting something, but if I remember it, I will tell you.