Well, the distributor is in correctly... I found TDC and the rotor points to the line corresponding to plug #1. Turns out I did have the spark plugs installed correctly (with the exception of 3 & 5.) Tried re-timing and even took the distributor out and went a tooth in each direction and no better adjustment could be made.
In short, the only way the car runs well and doesn't backfire is with plug wires 3 & 5 switched on the distributor cap. Could someone who worked on the car before I got here be masking a problem that lies deeper? Where should I look next?