You take something like chacha20 and use the disk block # to seek it, xor it with the data block and then encrypt it with a block cipher in ECB mode.
Would this be secure?
To avoid getting bogged down in implementation pitfalls lets consider an ideal scenario:
You have a constant size file (that is a multiple of block cipher size) that may get altered through time. Using a stream cipher to encrypt is therefore not secure under some threat models. So you combine a stream cipher with an ECB mode block cipher - through chaining, first xor with stream cipher output then pass through block cipher. Would this now be more secure? As secure as XEX/XTS?