Kubryk, I think you did the drawing perfect. The things you did
'wrong' (imho) was too short time intervals, and moving perpendicular to the target course. And perhaps you were too slow (submerged perhaps?). Note that it isn't really wrong, but it made the results less accurate than it could have been.
If you take more time between bearings the AOB calculation/drawing becomes more accurate. Do you remember how big the bearing differences were? Judging from your pictures I think they were about 5 degrees between 1st and 2nd, and 7 between 2nd and 3rd (or 12 between 1st and 3rd bearings), for the 29 degree AOB situation. Correct? Well, 2 degrees more than the first 5 is a bit crude, considering bearings are measured in 1 degree.
Using a bit of magic I profecise 
that if you had waited until the first bearing difference becomes 19 degrees, the 2nd difference (between bearing 2 and 3) becomes about 41 degrees. At the 3rd bearing the contact would have shown about 90 degrees AOB, and have the closest distance to your listening position. From 1st to 3rd bearing would have roughly taken 45 minutes. But that is a different kind of magic
:
time_1st_to_90AOB= 2*short_time_interval/(1- tan(AOB1)/tan(AOB3)
What I am trying to say here is patience is a virtue that pays well in accurate AOB and contact course. Perform some magic yourself, and see what variation in AOB you get for small deviations (0.5 degrees) in your bearings.
2nd point: You moved perpendicular to the contact's courseline. That does make you get closer to the courseline as quick as possible. But is that what you need? You really want to know where the 'virtual 4th' crosses the 'real 4th' line. For that to be accurate you need the biggest angle as possible between them. That means you need to start your move
perpendicular to the 3rd bearing. With the 'magic suggestion' above that would also be parallel to the contact course.
See in this picture (showing a pure intercept) how the bearingline would start to turn when your speed is completely perpendicular and greater, than his perpendicular speed component.
The quickest change of bearing is when you move in the direction where he came from (speeds on opposite side of bearing). But that could get him out of hydrophone range, and you need to catch up to it again later. If you move in the direction he is going (speeds on same side of bearing), and if you are as fast as possible (surface if you can), the bearing turns slower but still makes the 'virtual and real 4th' cross. Since the target is the one that decreases the range (remember you have no component along the bearing) the bearing-change will speed up over time.
Other than that, well done on your work.