Your only option is to use several of SPI SRAMs.
If you would consider parallel SRAM plus CPLD, include all the decoupling needed for the CPLD, plus programming header, some pullups/pulldowns, PCB area, effort to do the CPLD design, better power supply, that would provide enough current... Probably it's not the end of the list. I imagine you will need better than commercial grade CPLD, so check the price of the industrial one.
I didn't quite get the point. You have a microcontroller, that has the parallel memory interface, but this is already used for another purpose? Usually, those interfaces can be shared between multiple devices.