There were many design changes over the years to limit / minimize vibration / friendly harmonics issues in the SSME. Incremental progress. I have COMPLETE admiration for John Young and Bob Crippen for flying on STS-1. Engineers found MANY things on the Space Shuttle that could have caused mission termination if the exact wrong sequence of events had happened. As noted in your question there were years of improvements, description of incremental changes on the SSME's and (FYI) a "engine processing flow" description:
"Significant development was
required for the final configuration of the high pressure turbopumps. Fracture control was
implemented to assess life limits of critical materials and components. Survival in the
hydrogen environment required assessment of hydrogen embrittlement. Instrumentation
systems were a challenge due to the harsh thermal and dynamic environments within the
engine. Extensive inspection procedures were developed to assess the engine components
The LOX Pogo accumulator, for example, was put on the SSME because the Apollo program needed it. The SSME engineers didn't know if the Pogo accumulator was REALLY needed or not but it worked. See Apollo Pogo issue (as a side note I was told that the Pogo on the Saturn was so bad the center engine on the second stage was bouncing up and down on the cross and hitting the limits of travel):
"NASA announced that engineers had found a solution to the problem that occurred near the end of the Saturn V rocket’s first stage during the uncrewed Apollo 6 mission. During the last ten seconds of that first stage burn, the rocket experienced longitudinal oscillations called “pogo effect.” Pogo occurred when a partial vacuum in the fuel and oxidizer feed lines reached the engine firing chamber causing the engine to skip."
There was also the SSME LOX Post vibration issue:
"The definition of the critical flow velocity is addressed, and detuning of the vibrations of the LOX posts is discussed."
There were also issues within the turbines that were found and fixed, for example the Subsynchronous Vibration in the SSME HPFTP:
"SSME HPFTP hot-fire dynamic data evaluation and rotordynamic analysis both confirm that two of the most significant turbopump attributes in determining susceptibility to subsynchronous vibration are impeller interstage seal configuration and rotor sideload resulting from turbine turnaround duct configuration and hot gas manifold."
One of the larger issues on the SSME was that of Hydrogen Embrittlement. There were access ports on the SSME's to allow inspections of the known issues with minimal disassembly, so the engine didn't have to be COMPLETELY disassembled but yes, it was still inspected per Operational Maintenance Requirements Specification Document (OMRSD) requirements, I.e. "This part is inspected every 'X' flights" and of damage was found the part was replaced and sent out for analysis. The Hydrogen Embrittlement issue was described in this 2010 conference paper:
"From the humid, corrosion-friendly atmosphere of KSC, to the extreme heat of ascent, to the cold vacuum of space, the Space Shuttle faced one hostile environment after another. One of those harsh environments the hydrogen environment existed within the shuttle itself. Liquid hydrogen was the fuel that powered the shuttle s complex, powerful, and reusable main engine. Hydrogen provided the high specific impulse the bang per pound of fuel needed to perform the shuttle s heavy lifting duties. Hydrogen, however, was also a potential threat to the very metal of the propulsion system that used it. The diffusion of hydrogen atoms into a metal can make it more brittle and prone to cracking a process called hydrogen embrittlement."
Does that answer your question?