The situation is already “almost impossible”. The schools where a 1340 is the 50th percentile, where your chances of getting accepted are higher, are not in a position to offer more than a token amount of financial aid, much less a full scholarship. That’s the dilemma that all international students face.
If your teachers and guidance counselor will write in their letters of recommendation that you took the highest level classes your high school offers, then the colleges will not penalize you for not having AP classes.