The 2Mb and 4Mb dual ports are a newer generation and family of devices versus the 1Mb device. As you can tell by the datasheets, they are very different devices. Where the CY7C09579V device can run up to 100MHz, the CY7C085xV can run up to 167 MHz. The features on both families differ widely as well. The pure density as well as complexity of these devices drives the current higher.
Looking through multiple NVRAM controllers, you are correct in that most can't handle more than 150 uA of battery current. I would guess that a battery would not be a good backup for the dual port RAM, as it would die very quickly with such a high current draw. The battery would need to be replaced very often.
An alternative solution (which would really depend on how often and for how long you foresee power fluctuations) could be the usage of slow discharge capacitor. This way, every time the power going to the dual port is cut off, the capacitor can sustain the memory for a short amount of time, and when the power is re-established, the capacitor will charge again. The circuitry for this would be pretty large, but it will allow you to "re-charge" the capacitor over and over again.
Another possibility, also depending on your application, may be just using two 1-Meg dual port RAMs and cascading them depth-wise. This will double the density and each dual port could have its own NVRAM controller.