I started this post back in October when I actually finished the work, but I forgot to post it then. So here it is now.
Three million wires later, my 8-bit full adder is complete.
Here it is with the front panel attached. I use the front panel in lieu of switches and LEDs.
Here's the circuit by itself:
Each pair of columns calculates four bits. Each bit needs nine gates, and consists of two dedicated 7400s (actually 74HCT00s) and a quarter of a common 7400. If we number the ICs in column-major order, bit 0 is calculated by ICs 1, 2, and a quarter of 3; bit 1 is calculated by ICs 4, 5, and a quarter of 3; bit 2 is calculated by ICs 6, 7, and a quarter of 3; bit 3 is calculated by (wait for it) ICs 8, 9, and the final quarter of 3.
Due to layout weirdness, bits 0-3 are calculated by the right pair of columns, while bits 4-7 are calculated by the left pair of columns. I'd love to say the vertical offset is intentional, but it's actually due to a layout mistake or change in plans, the details of which I've since forgotten.
Wiring this thing up was mind-numbing, but it was awesome to see it come to life (I tested each bit after I wired it up).
Here's the schematic. My original intent was to build a 4-bit adder, but I had so much fun wiring(!), that I decided to do it twice, for 8 bits.