So it seems, like all convergence issues, I have 3 choices.
1. I can set the convergence at the point where I find I'm getting most of my target shots in the K4, which is around 200.
2. I can set the convergence at 600 to try and improve my distance shots, compensating for loft when I take close in shots.
3. I can set for around 300 and split the difference.
Regarding option 3, at setting 300, is there much loft at 200 and is there much drop at 400?
Laziness will practically ensure you get a bunch of misses when it comes to gunnery, plain and simple. There's no "magic" answer to your question, so no tidbit of advice will allow you to be lazy and successful at the same time.
From an "aim-point" perspective, you have it pretty easy with a nose-mounted gun, because it's mounted so close to eye-level and the trajectory "behaves" the way you think it should. It makes the trajectory behave the way Fugitive states-
If you set the convergence at 600 you will hit ABOVE center at 300 due to the lob.
With wing-mounted guns though, his statement isn't necessarily true though. With a 600yd convergence you'd hit LOW at 300 with the F4U's .50's, for example.
What makes it difficult to get hits with the 30mm's is the time or "space" between the rounds. Due to that, having a "perfect" convergence setting, along with "perfect" aim, is far from enough to ensure hits. You also need to time your shots perfectly, unless your target is going straight away and has no apparent motion from your perspective. An absolutely perfectly-aimed shot on a crossing target will miss every single time, if you squeeze the trigger a fraction of a second too early or too late.
The three convergence options you mention are only valid for discussion assuming you have the required timing down, or are shooting at targets that appear stationary.
Assuming you're doing that, what are the merits of each of the options you list?
1- Pro's... targets are bigger when you get closer. Less time is required for the round to travel a lesser distance.
Con's... A convergence set in super close doesn't take advantage of the trajectory to it's fullest. It's like sighting-in a center-fire deer rifle at 100 yards. It work's, but isn't optimal. It leads to more guesswork at a larger variety of ranges.
2- Pro's- It'll let you aim directly at
some targets at 600yds.
Con's- You may need to adjust your aim-point for every other shot distance. It may actually be harder to hit a target at 200-300 yards, than it would have been to hit one at 600 with a 300 yard convergence.
3- Pro's- It's about as good as it gets when looking for an overall "good" option for the largest range of shooting distances. Aim a little high for long shots, maybe a little low for close (but it probably won't really matter) shots.
Con's- it still won't allow for the differences you'll see in impact point for firing while in anything other than a straight and wings-level 1G configuration. Firing while banked, inverted, nose up- or nose-down, or pulling anything more or less than 1G will render your sights inaccurate.
Regardless of the convergence you choose, the beauty of the matter is that for us, any laziness you exhibit in learning about aerial gunnery is to our benefit. In the end, it means that the best, most accurate, and most truthful answer to your question is "It just doesn't matter".