Can prepending "junk" be equivalent to an IV when encrypting using CBC?
If you know that the integer is fixed in size (always in the range 1-1000), then the second approach is fine.  Effectively, you still have a random nonce (what you are calling the "junk"); you concatenate the nonce and the integer, then encrypt the result with AES-ECB.  This works.

Do make sure that you choose a large enough random nonce.  I recommend making it as large as possible, i.e., filling the full remaining width of the block.  For instance, if your value is always in the range 1-1000, then it will fit in 10 bits.  So dedicate 10 bits to hold the value, and use the other 118 bits for the random nonce (i.e., to encrypt, you generate a random 118-bit nonce, concatenate it with the value, and then encrypt using AES-ECB).  At a minimum, you probably want your nonce to be at least 80 bits long, and a bit longer might be a bit better.

Also, make sure that you use a cryptographic-strength PRNG to generate the random nonce.