Yeah, I'll try. Gimme a couple of days?
It's always that "give-or-take 90*" you mention, I've experimented enough to prove that your 're-emergence' is on one face of a 'virtual cube' (probably a more complex geometry, but let 'cube' suffice huh?) surrounding the station, dependant on your approach vector. WHERE on the face seems to have no correlation to the accuracy or velocity of the approach, nor does the 'drop' distance (tested from 997Km down to 231Km) so it's probably an RNG mapping to an 8x8 (guess) grid on the face.
In any case, you can see the slot right away, aim the nose for a point 3km in front of the axis, hit the booster, go to systems & set up to trigger permission to land at 7.49Km, then as soon as the distance-to-target slows right down or stops - turn to the target marker & Voila! Lined up on the slot