David- thanks! I'm starting to think something is wrong with this unit, but maybe it's just not that intuitive.
Edstrom- as OG said, you need more info to go from that pic to the ROM dump. On two sides of the ROM array are circuits that select the row and columns for the selected byte. For this chip, you can see them above and to the left of the ROM array in this pic: http://www.seanriddle.com/tnt8012acid.jpg The circuitry above selects the page and the bits in the byte, while the circuitry to the left selects the byte in the page.
That circuitry was a bit overwhelming for me to decode when I started, so I took a picture of a ROM that Kevtris had already dumped, and figured out how the bits in the picture matched up to the bits in the dump: http://www.seanriddle.com/mp3438a_rom_acid.jpg
The lucky thing is that so far, all the TMS1100s have had the same ROM array layout, so the same process decodes all of them. In fact, the ROM arrays are extremely similar between the different TI microcontrollers.
I played with a USB microscope for a while, but the resolution was not high enough for me to decode the bits.