Combining CTR and ECB modes to prevent attacks
There are a few problems that spring to mind:

this is a double-pass scheme, which is computationally expensive;
the leakage of blocks that are identical is unnecessary, there are schemes that only leak fully identical plaintext;
ECB mode requires padding, so you would create some overhead.

Now you could argue that 1. is not a problem on current computers. However, that would only be a good argument if there weren't any schemes out there that would present the same properties without requiring a double pass.
As for 2, there are schemes such as Format Preserving Encryption that don't leak any information other than fully identical plaintext. FPE is generally rather expensive when it comes to implementation (on the other hand, not having to store an IV is generally not a problem for large binaries as they would generally have a VARiable size). Another option is to perform a block encrypt on the index and use that as unpredictable IV for CBC mode (possibly with ciphertext stealing if you don't like the padding overhead). Existing disk encryption routines such as XTS and ESSIV have already been mentioned.
As for 3, ciphertext stealing (CTS) for ECB mode can of course be implemented, but it definitely doesn't help with ease of implementation, which would be the major benefit over other schemes (ECB is generally available in e.g. SQL, and CTR is relatively simple to implement using ECB, although I definitely would not like doing so in SQL).
Finally, if you have room for an authentication tag, then a SIV mode (such as AES-GCM-SIV) could be used to remove the need for an explicit IV. If you've got room for both then just a generic AES-GCM would make sense of course.
All in all, I think that - while the scheme has merits - there are better options out there - preferably ones that are build into the DB engine.