Finally, your statement that the failure of any one of the first stage engines would cause ocscilations that would destroy the airframe is simply not true. there was a primitive control system specifically intended to keep thrust on all sides of the rocket even, and by the final flight it worked pretty well.
"First failure, serial 3L
February 21, 1969: serial number 3L – Zond L1S-1 (Soyuz 7K-L1S (Zond-M) modification of Soyuz 7K-L1 "Zond"
spacecraft) for Moon flyby.
A few seconds into launch, a transient voltage
caused the KORD
to shut down Engine #12. After this happened, the KORD shut off Engine #24 to maintain symmetrical thrust. At T+6 seconds, pogo oscillation in the #2 engine tore several components off their mounts
and started a propellant leak. At T+25 seconds, further vibrations ruptured a fuel line and caused RP-1
to spill into the aft section of the booster. When it came into contact with the leaking gas, a fire started. The fire then burned through wiring in the power supply, causing electrical arcing that was picked up by sensors and interpreted by the KORD as a pressurization problem in the turbopumps. The KORD responded by issuing a general command to shut down the entire first stage at T+68 seconds into launch. This signal was also transmitted up to the second and third stages, "locking" them and preventing a manual ground command from being sent to start their engines. Telemetry also showed that the power generators in the N-1 continued functioning until the impact with the ground at T+183 seconds."
As it relates to the 4th and final launch:
"Fourth failure, serial 7L
November 23, 1972: serial number 7L – regular Soyuz 7K-LOK
(Soyuz 7K-LOK No.1) and dummy LK
module-spacecraft for Moon flyby
The start and lift-off went well. At T+90 seconds, a programmed shutdown of the core propulsion system (the six center engines) was performed to reduce structural stress on the booster
. Because of excessive dynamic loads caused by a hydraulic shock wave
when the six engines were shut down abruptly, lines for feeding fuel and oxidizer to the core propulsion system burst and a fire started in the boattail of the booster; in addition, the #4 engine exploded. The first stage broke up starting at T+107 seconds and all telemetry data ceased at T+110 seconds. The launch escape system activated and pulled the Soyuz 7K-LOK to safety. The upper stages were ejected from the stack and crashed into the steppe. An investigation revealed that the abrupt shutdown of the engines led to fluctuations in the fluid columns of the feeder pipes, which ruptured and spilled fuel and oxidizer onto the shut down, but still hot, engines. A failure of the #4 engine turbopump was also suspected. It was believed that the launch could have been salvaged had ground controllers sent a manual command to jettison the first stage and begin second stage burn early as the stage failed only 15 seconds before it was due to separate at T+125 seconds and it had reached the nominal burn time of 110 seconds according to the cyclogram.
When I read that, it screams to me, "worked pretty well"