I checked the most common AES modes and I think I got the goal of them: avoid same cyper text for same plain text. However all modes except ECB have the weakness that lost part of the message stream will result in a broken decryption because the key can not be generated. CFB is one attempt to resynchronise, it needs the previous cypher block and CTR is another way, if you know how many blocks are missing.
I am not a specialist in cryptography but I would like to suggest a extended use for ECB: Would it be appropriate to split each block into a part with plain text and another part with true random data in order to assure that each cypher text will be different from the other while keeping the same key (ECB mode)? Of course I loose plain text capacity and safety depends on the ammount of random data. Lets say the first 10 bytes of each block are plain and the last 6 bytes are random content. That means that I reduce the randomness from 2^128 to 2^48 which is still high (and it applies only if I allways have the same plain text).
Is this an acceptable safety? OK, reply attacks are possible and need to be handled separately.