Thanks for all the replies, folks.
About the CompactFlash option, that's a good idea. Although I will need to read as many data as I can per second, and I am wondering what the limit is for writing to flash. The last time I looked at flash, many years ago, the write speed was low. But then these days I know it is faster.
Also, there is a Circuit Cellar project that does just that. The guy connected a PIC processor to a CompactFlash socket, using the 8-bit access mode of the CompactFlash standard rather than the IDE approach. So it is slow, but the idea is clever.
About microcontrollers with lots of RAM, I discovered one that is intriguing: the MRM (Mini Robot Mind). It's here:
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It can take up to 1 meg using a daughter card and the guy who produces it is about to release a daughter card that takes CompactFlash. The main board is only $99 and has a 68332(?). The only comparable thing I know of is a discounted 386SX board that I found, which is not quite as good for me although I suppose it would run Linux.
Thanks again...