that's along the lines of what I was thinking, along with reducing complexity and weight...
If you could get it to fire 3-400 rounds per minute and add some sort of a powered mount as well...
then what about a smaller version to put on PT boats? sort of like the three tube 20mm used on Cobra gunships? Would have played havoc as a Motor Gunboat weapon...
The technological bottleneck was mostly powered mounts. The technology for powered AA mounts was new, first adopted about 1930. The typical power available in 1940 was just few kilowatts or even fraction of kilowatt per mount, and size scaling problems were severe.
Following problems happens:
1) Rotary gun on motorized mounts will exert a significant gyroscopic forces on its mount if steered
2) To counter these forces, either counter-rotating flywheel or oversized traverse/elevation actuators are used, in both cases increasing mount weight.
2) Increased recoil due high fire rate forcing further over-sizing of mount mechanical parts
Overall,
1.1-inch Gatling (rotary) motor-steerable gun mount in 1940 will weight more, will be prone to failure, expensive, maintenance-heavy and less autonomous compared to a battery of automatic cannons of same firepower.
It is
not an accident the first modern applications of Gatling (rotary) cannons (including M61) were on fixed mounts. Technology for rotary gun on motors-steerable platform was likely not practical until at least 1960, when much more lightweight and reliable motors, solid-state control circuits and stronger mechanical parts would be available.
Regarding
non-motorized 1.1-inch Gatling mounts, these are definitely not manageable. Even much lighter and 1-inch automatic cannons required a heroic levels or above of physical strength to operate fast enough to track incoming aircraft, as Japanese experience with Hotchkiss-derived 25mm cannons demonstrated.
20mm manually steerable Gatling cannons around 1940 are theoretically possible, although
1) These would be short-ranged enough to only retaliate to torpedo or dive bomber which already released ordnance
2) Accuracy will be extremely marginal due gyroscopic effects, resulting together with high rate of fire in ammo shortage. I remember IOTL Japanese were limited in 25-mm mounts installation by ammunition supply, not by number of available guns. Going to have much worse ammunition shortage with rotary cannons, may be even beyond capability of more capable states like British.