You’re in a tough spot with your requirements. Higher end microcontrollers with EBIs can meet your 10MB/sec acquisition rate but will be hard pressed to efficiently interface with the amount of memory you require. As you transition into the world of microprocessors which have the bandwidth and resources to work with memory other than SRAM, you start being burdened by the potential need for an OS of some sort.
What exactly are you trying to do and are you sure there isn’t a more efficient way of handling your data instead of buffering your entire capture and writing it afterward?
I know you don’t want to do logic design but a sub $100 FPGA board could acquire your data and simultaneously write it to an SD card without having a huge amount of onboard memory.
-Bill