Most RAM for an MCU in a DIP package

If you only need the DIP format for prototyping, use some adapter boards and prototype with those. With a steady hand you should be able to solder SOIC and TQFP parts.

This kind of thing:

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If you just need extra RAM, and you don't need to address it directly as a memory address (i.e. okay to go through a function call), Microchip makes a 32KB SRAM with a 20 MHz SPI interface in an 8-pin DIP (also available as a SMD) for $1.66 in singles, $1 in quantity.