I found the below quote and source. But as you said unfortunately there is not a ton of information on this topic.

" Fully armed B-29 versions featured five gun turrets -- upper forward and aft, lower forward and aft, and a manned tail turret. Each turret mounted two guns, except for the upper forward, which had four. All turrets were electrically powered (the B-29 was an electric airplane with more than 100 electric motors, including landing gear actuation), remotely sighted and controlled (no in-flight gunner access, including the tail turret), electro-mechanical computer directed, with manually fired guns.

General Electric developed the Central Fire Control system, which consisted of five interconnected electro-mechanical analog computers, one per gun turret. Each gunner could directly fire his own guns if the computer system was inoperative. All gunners had control of their turret and secondary control of others -- an intercom system provided communication between the gunners. A gunner could fire the guns of another turret from his sighting position, and, uniquely, fire the guns of two or more turrets at once.

Thousands of these computers were manufactured for and utilized by B-29s. This program, then, represents the first mass production and use of electronic computers, although they included mechanical components and thus were not purely "electronic."

The defensive armament system proved successful in combat, and was exclusive among the combatants during the war. On January 27, 1945, the B-29 identified as "B-29 A Square 52" scored 14 kills over Tokyo, Japan, as follows: rammed by two fighters, gunners then shot down 12 more fighters, the damaged bomber flew 1,500 miles back to Saipan on three engines, crash landed, all crewmen survived, but the aircraft was written off. This is probably the highest number of air-to-air kills by a single airplane during one mission. "

http://www.historylink.org/index.cfm?DisplayPage=output.cfm&file_id=3828

I have an extra question – just how did this fire control system work?

I have watched this video and understand the basics of the turrets being slaved to the sights. But how did the sights work? Would the guns simply turn and elevate/depress while mirroring the movement of the sights?

Or was it more complex, and all the turrets were actually somehow calibrated to the sights? Meaning that the sights could be not only moved, but also ranged, and the turrets were not actually copying the sight movement, but would rather turn towards its target?

Not sure if I'm making myself clear, so I drew a picture. Would two lines drawn from the sight and the turret guns be parallel, or would they intersect at a point indicated by the sight? I'm trying to wrap my head around how would they control more than a single turret at a time and only the latter makes sense to me.

Finding any accurate numbers is going to be next to impossible.

Aircraft kill claims are notoriously and wildly inaccurate, especially in the case of bomber crews making kill claims.

Fighter aircraft kill claim counts tended to be more accurate because generally you you had one aircraft firing on the targeted aircraft at a time. So the lead pilot may take the shot, and have his wingman as a witness. Fighter aircraft were also much more likely to have gun cameras installed which would give filmed evidence.

Bombers on the other hand are a completely different story. First of all, and this is especially true of the giant Allied bomber streams, you often had multiple aircraft firing at the same target. So even if a fighter is definitely destroyed, you may have five different claims for that single fighter, without it being recorded as a shared victory.

Another major problem is that bombers, unlike fighters, couldn't really follow their the claimed kill all the way to the ground. As such, a turret gunner may score some hits on a fighter, and then watch as it dives for safety while spewing some smoke from burning leaking oil and assume he just scored kill. In reality however, its quite possible the fighter just suffered non fatal damage and returned home just fine.

And while the inverse may be true - in that a gunner might see a fighter peel away trailing smoke after scoring a few hits, only this time he may assume the plane made it home okay when in fact the pilot ended up bailing out shortly later - this is far less likely. Bomber crews (and fighter pilots as well) tended to be overly optimistic about their success as opposed to being cautiously realistic.

Kill claims should never be taken at face value, and need to be backed up by solid evidence. Ideally this would mean having gun camera footage showing catastrophic damage such as a wing being blown off, a major fuel tank explosion, or the pilot bailing out. Or having ground forces being able to physically inspect crash sites of downed aircraft, etc. And one of the things the Allies did after the war was pour through the Luftwaffe and Japan's records in an attempt to see just how accurate, and likewise how effective, their claimed successes really were. While all sides used inflated numbers for morale and propaganda reasons during the war, having access to the actual log books, inventory books, maintenance records, etc, that were used internally for logistical reasons offered them valuable and much more accurate information in regards to enemy aircraft losses on a specific day to day basis in specific geographic areas that could be compared to their own records for verification.

But even then the problem exists that all too often, those records may only indicate that an aircraft was lost on a specific day, without giving much useful info as to the cause of the loss. Now, while the B-29 served only in the Pacific, we see the same problems on both fronts when it comes to record keeping. As the war dragged on, records in some cases became increasingly less accurate and detailed in some cases. This is important because enemy damage only makes for one particular cause for aircraft losses. Pilot error, mechanical failures, and other such accidents can sometimes (depending on aircraft type, role, etc) account for more losses than enemy action. So, lacking detailed accounts of aircrafts' fates, enemy records of a loss of an aircraft in one sector on a specific date may inadvertently backup a claim of a kill if the record does not one accurate note of the specific cause. Of course, they might not always know the specific reason either. But the reason I mention this, is because as the war went in, both Japan and Germany suffered from an ever shrinking pool of experienced pilots, and their new recruits enjoyed less and less training. Also, quality control, subpar manufacturing, defects in both raw materials and subsequent finished products, also contributed to increased losses.

And going back to training, inexperienced pilots with little experience and training are possibly going to make any such systems seem more effective than they might actually be due to making mistakes and not knowing the proper ways to attack. For example, an inexperienced pilot may make an attack from dead astern in a "slow and gradual" manner that gives the bomber's defensive armament a simple and easy target to engage as opposed to attacking in a manner that may be more likely to overwhelm the defensive armaments capabilities.

Anyway, just to give an example of how drastically different the records of two different sides may be, there were instances of Allies bomber formations returning from a mission having claimed dozens of kills. After the war however, Luftwaffe records indicated that only one or two aircraft were lost on that particular day in those particular areas. Admittedly, I'm more familiar with the Luftwaffe vs Allied bombing than I am with the Japanese vs Allied bombing, but I do know that great disparities existed in the Pacific front between reported and actual kill counts.

(apologies for the poor formatting and somewhat rambling nature of this post, I'll try and clean it up and make it a bit more concise and coherent if it's not clear what I'm trying to establish)