Synchronization gear

Apparently pilots who were a good shot benefited significantly from being able to place many bullets in the target.

In the article it mentions ace pilots who chose very close convergence distances.

First of all, the propellers on some of these larger planes are pretty huge. Look at this schematic for a Corsair... the propeller sweeps out an area that's like three times larger than the fuselage. You could easily be firing to the left and to the right of the enemy without actually hitting anything: https://drawingdatabase.com/vought-f4u-corsair/

Actually the problem is even worse than it looks for the Corsair because this is a relatively fat plane with a huge propeller, fighting svelte Zeroes and 109's.

Next, sometimes the guns have to be spaced further out than you'd like them to be because of other constraints like the positioning of the wheel wells for the landing gear. The Spitfire has pretty wide-mounted guns as a result: https://drawingdatabase.com/supermarine-spitfire/

Regarding the difficulty of making the shot: you're right, it's very hard to hit a propeller-sized target at a relatively close 300m. If you're both maneuvering, you have to lead the target while compensating for bullet drop, gravity, side-slip, g-loading, convergence, etc. So the general approach is to envision a circle where you think your aim needs to be (based on all those factors above), start firing at the bottom of that circle, then gradually pull up and sweep your fire through the middle and top of the circle. The better your aim, the tighter you can make that circle and the quicker you can sweep through it. The poorer the gunnery characteristics of your aircraft (gun accuracy, rate of fire, convergence, number of guns, etc.), the larger that circle has to be--even if you otherwise have great aim.

If your guns are parallel, or set to a convergence that doesn't really match the current distance to the target, the trick above doesn't work. You'll just send a wall of bullets to the left of the target and another wall to the right, but have nothing hitting the tail. You might hit a wing if you're lucky, but wings are extremely thin from a rear aspect and one or two 50cal's isn't going to rip off a wing anyway.

So that's why center-mounted, or at least wingroot-mounted guns are much more comfortable to aim; there's just one less factor to compensate for.

On the other hand, one notable disadvantage of firing through the propeller is that the synchronizer reduces your rate of fire a bit. Whenever the gun is ready to fire but a propeller blade is coming up, the gun has to idle for a bit. Guns mounted further out can just fire at their maximum rate.

(Of course, on the other other hand, mounting heavy things like guns and ammo boxes further from the fuselage reduces the plane's roll rate, which you need to line up the shot in the first place! ... I'll stop here)