I'm thrilled to finally be able to demo a working program! Click the GIF above for higher quality.
This is a demo of TOM-1 loading the value 0x01 into the TOS (top of stack) Register, then adding TOS to itself every other clock cycle to produce a marching LED sequence (lower left, as well as the alphanumeric display). We are only cycling through the high 8 bits in this program for this demo, but TOS is two bytes wide and can support cycling through 16 bits.
The most complex task has been building out the ALU. It's a 16-bit bus, and because the pin layout on the 74LS283 (4-bit add with fast carry) and 74LS00 (quad NAND gates) are staggered, wire placement took a lot of consideration. The chips are fairly crammed in on the rightmost circuitboards, so this took a few stages of wiring: first pairing each chip's inputs and outputs together (purple/grey wires), then wiring connections 4 bits at a time to the TOS Register, the Memory Bus, and the 16-bit output (yellow/red/orange); then wiring the TOS Register and Memory Bus lines to the 74LS573 latches where the ribbon cables from the left side are connected (green wires). This goes on to latch to a 16-bit value that can be loaded from ROM.
While it's referred to as a Memory Bus, none of the memory is actually hooked up yet: the 62256 RAM chips and the 6116 Stack chips aren't connected yet. TOS has a latch to copy its value onto the Memory Bus, normally so that we can load the TOS register into memory, but in this case we turn it on to let us add TOS to itself (like an assembly-level "double" opcode). Since there's only one real CPU register, there's not much to do until the stack is connected. But I'm thrilled to finally run blinkenlights :)
Source code of the program [4 bytes per opcode]: 0x02 0x00 0x00 0x01 0x00 0x00 0x03 0x00 ... (last four bytes repeat eight times, then Arduino resets)