Which kind of Flash supports "Bit-alterable write operations" right now?
Rethink the application to determine how you can use a smaller amount of the memory in the application. Quite possibly the part being replaced was 128 Mbit simply because the technology steered toward parts of that density and not that the product application actually requires that size of storage.

Algorithms that use individual bit level programmability are far more likely to be random access across a smaller storage space than typical large block organized Flash memory devices.

FRAM Technology may very well be what you want to take a serious look at. FRAM reads and writes at the bytes and bits level (for bits you need to perform a read-modify-write operation). FRAM has no long multi millisecond write / erase times. Writes typically take place as fast as the serial interface can operate. FRAM also has impressively high write endurance numbers. Cypress has a SPI interfaced FRAM device that is 4 Mbit (512K bytes) that should adapt well. You can also consider placing multiple devices to increase storage a bit.