Well, my ride home yesterday wasn't successful. I did get home, and it only took twice as long as usual, but sadly my first attempt to go traffic-light-less just didn't work out. Even though I had a pretty useful scrap of paper with cryptic notation concerning the streets and intersections I planned to use (nose in the map is not allowed, but consulting a scribbled sheet on the fly is OK)
I did reduce the number of traffic signals to six, but also including a few non-legal maneuvers. My real failing was in my clever attempt to avoid traffic signals by (legally) riding in parks. However, I failed to notice that nearly all of the park entrances were protected by traffic signals (so that park users can enter and leave safely, I guess). This was even the case where motor vehicles were quite clearly prohibited. My no-backtracking rule also left me at two park exits, facing a traffic signal, and unable to backtrack and try a different exit.
There were also a couple of places where bicycle riding isn't quite kosher but this is not apparent from the map. Mostly pavement/sidewalk riding, albeit very briefly (e.g. Woburn Walk, which looks like a road on the map, but is quite obviously pedestrian-only. I should have remembered this, working just around the corner. Or another road which dead-ends, and the only place to ride is across a pavement/sidewalk onto the adjoining road). The only other rule-breaking occurred when I saw a traffic signal ahead and had no place to go but the wrong way on a one-way street (maybe a very good possibility in the other direction, though, as long as I can solve my "park problem").
So yesterday's score is 5 traffic lights, 4 riding in pedestrian areas, and one "wrong way". I think I can do better, but some more obsessive-compulsive behavior will be necessary.