EPROM Replacement Strategies
I'm seeing &lt;5MHz clock rates listed for that micro, so I would be very tempted to get a modern micro with a high enough pin count and 32K bytes of spare internal flash, and emulate it in software.  With a 3-wire serial port hanging off the end of course!  

Major challenge I see would be 5v - 3.3v conversion.  You could probably do it with series resistors, assuming that the output of the 3.3v micro is enough for a reliable read by the old micro (which it usually is, if you aren't in a high-noise environment)

If the clock is low and you don't need the full capacity, you might be able to use an ATMEGA328 running at 5V.  

I guess another challenge would be insuring that the add-in comes out of reset first, though you could fix that with a jumper wire to hold the main processor in reset until the new device comes out of power-on-reset.

Of course another option if the processor is socketed is to emulate the processor rather than the EPROM.