I have completed my experiments with the Prototype 7 Power Supply.
Here is the schematic.
I have left out the multiple output stages and concentrated on the +5V output. The trouble I was having before stemmed mostly from the transformer construction. Specifically, the leakage inductance was way too high for the size of the primary winding inductance. This was causing large spikes in the current through the sense resistor which would, in turn, tell the controller to turn off. By increasing the inductance and reducing the leakage inductance, I was able to get stable output regulation.

The trick to doing this experiment on a breadboard is to work hard at controlling the leakage inductance of the transformer. I tried several different winding techniques. Two things made a huge difference. First, a 'progressive' style of winding is much better than a 'straight' style. The difference is well explained in section 3.5.9 of Marty Brown's book (The Power Supply Cookbook). In short, say you have to do 90 turns to make a transformer. Furthermore, say the bobbin you have selected only has room for 30 windings. It is much better to wind three turns vertically (one on top of the other) than it is to wind and entire row, then overlap another row and finally overlap another row (to make 3 x 30 = 90 turns). The reason for this is that with straight winding, by the time the second row returns to overlay the first winding (so turn 60 is overlaying turn 1), the voltage difference in the wires at that point are large (assuming the voltage drop across the transformer is evenly distributed). This creates a capacitance between the two windings that increases the leakage inductance. Notice that except in the middle, just about every winding in a straight winding approach has this problem. Alternatively, if you just 'scrunch' all the windings on top of one another (as best you can) and progressively cross the bobbin such that turn N, turn N+1, turn N+2, ...etc are right next to one another, then the leakage is greatly reduced.

Secondly, splitting or doubling the winding between the inner core and the outer layer of the bobbin reduces leakage. Say, for instance, that you need to do 60 windings. By putting 30 as the inner winding and 30 as the outer winding and connecting the serially the leakage is reduced. Alternatively, you can put all 120 windings on the inner layer and then do another 120 windings on the outer layer and connect them in parallel. This last approach (parallel windings) seemed to work the best but required a lot more wire.

New Layout. Here is the new layout. It was suggested on the diyAudio site that I try to compact my design to reduce some of the noise. I had mixed success with this but it makes for a cleaner looking design. The parts that still have their 'legs', in general, are snubber part that I am constantly playing around with so I don't trim them down.
Vds and Ids. This is an example of Vds and Ids at medium load. Notice that I still have a lot of dv/dt trash but it isn't as bad as it was before. By increasing the inductance of the primary winding and reducing the leakage inductance, I was able to make a stable output.
Vds and Output. This is an example of Vds and the +5V otuput at medium load. I still have rather large spikes in the output but I believe I could get those under control with better construction (better xformer and a PCB).
Vds 'Bump'. I still get some unexplained behaviour. In this picture, notice that I get a 'blip' or 'bump' in the Vds just after a successful cycle. This is caused by a false trigger of the gate. That false trigger appears to happen when I get a 'ground bounce'. My ground and voltage rail coming from the rectifier section seem to get a rather large spike which messes up my 5 volt reference from the controller. Bouncing that reference (and the ground) will cause the voltage at pins 1 and 2 to cross momentarily which is what makes the gate fire. I don't know the cause of this but I felt it was time to move on to another design.