For destinations with a letterbox, always approach the station from the nearest planet. This will usually give you a decent alignment to the letterbx.
I usually aim for 0:06, try to get a good angle on the destinations orbit, top/down with a nice circle drawn around the planet is perfect. Then I aim the ship between the planet and station. Full throttle at about 1350ish KM/s, this usually drop to under 1000 when in range.
If I see I am about to overshoot, I just drop nose, get destination at a good angle and circle it until 0:06 again. If this happens when closer to station, I try to do a circle 90 degrees on station and planet, inside the stations orbit. This makes it easy to align for entrance once speed bleed off.
Can someone confirm for me, are the concentric blue rings around planetary bodies the gravity well? I find if I steer just outside of those I can approach at a faster speed, as I suspect that I'm not experiencing any acceleration due to gravity and overshooting.
While it is possible to "exploit" the eta as the OP described, the feature itself is broken until it factors in the automatic speed adjustments by the computer.