Slowly but surely.
After much agonizing and after asking lots of questions to a lot of people (thanks Jan W, Ben, Gary et al) I finally decided on a 27 degree steering head angle (also known as rake). However, (and this is very counter-intuitive to me) the rake has little influence on how the bike steers. That is decided by the "ground trail". Ground trail is defined as "the distance the contact patch of the front tire lags behind the point where the steering axis intercepts the ground". The longer the trail, the more stable/slower your bike will steer. I'm aiming for 100-110 mm ground trail, which will keep the Swedish authorities happy. They won't pass anything with too little trail. Anoraks can read more on the subject here.
After that it was mostly a case of making sure that the front wheel would fit in front of the downtube, and that there was room for the radiators. I know the slope of the top tube looks weird, but in order to get the tank to sit correctly it has to look like that. The next piece of tubing to be added will be an almost horizontal tube tarting from where the downtube meets the steering head and going back - completing the triangular structure that will keep the steering head in check (and which will be mostly hidden by the tank).
And this is how the steering head turned out after about 90% of the metal was removed from that huge metal ingot (see below). It now houses the new bearing races, and mates perfectly with the steering stem of the GSX-R750 K7 forks. Nice huh?