We only know that Soran developed a way to affect the Nexus trajectory.
Almost any decent scientist within the Federation and with same goals as Soran would likely be able to achieve a same effect.
The movie never really portrays if Soran's civilization was much more advanced compared to the Federation of the 24th century.
Remember, the Feds were able to pretty much catch up to everybody in the AQ and BQ by the 23rd century.
In the 24th, their technology was considered to be most developed compared to the neighbors (at least in TNG era as per Q himself), and rivaled decently with numerous DQ races (including the Dominion ... at least just before/for the duration/after the war).
True that it's a question if Soran's tampering would be detectable ... Soran was working for the Federation (or that's the impression I got from the movie) for a long time and would likely be aware of numerous standard procedures ... however, the crew of the Enterprise knew what Soran was trying to do and that he was on-board the BoP, along with the fact Ursa and Be'Tor were not conventional Klingons.
In my perspective, the writers goofed up big time. If the battle was fought between an upgraded/modified K'Tinga or Vorcha class ship, then the battle would have been more convincing ... a BoP is stretching it a lot with 0 explanation behind the whole 'farce'.
When the Klingons noted their shields were holding, that's just something that happens in battle (doesn't mean their shields didn't lose % during the hit).
Even an old ship would be able to withstand a hit or two before falling into submission.
Within the confines of Trek universe, the BoP should have been destroyed very fast.
Fact remains that Riker knew the Enterprise-D was compromised with it's shields down, and I still don't understand why he never simply unleashed a full barrage onto the ship (maybe if it was explained that the BoP disabled their weapons with first several hits ... then it would likely pass).
In an alternate timeline, the battleship Enterprise was able to destroy a K'Vort class ship (larger/more powerful BoP with raised wings) with several torpedoes and phaser shots. It's very likely a measly BoP (even with some upgrades) would fair extremely poor against a Galaxy class ship.
Rotating shields very fast was done by Data in BoBW for example during the confrontation with the Borg which repelled their draining tractor beam.
It didn't affect the hardware in any capacity, and it definitely wouldn't later on since the technology in question underwent upgrades ever since BoBW and would likely be able to do so even faster (not to mention make it part of standard combat operations ... at least, it would be the sensible thing to do).
Shield modulation/frequency changes worked well against the Borg initially in TNG ... and again in 'Dark Frontier'.
It just depends on how fast you can rotate the frequencies to be able to stay ahead of the Borg and prevent them from adapting (at least temporarily) which gives you an opportunity to strike back.
The Dominion was a different story because they utilized phased-polaron beams.
If the name alone is any indication, then it stands to reason no shield modulation worked because the nature of the weapons was different (perhaps it was able to achieve partial phase) compared to phasers/disruptors/borg beams ... which is why no frequency changing would work. The shields would have to undergo re-fit's in order to compensate for the phasing effect automatically.
I think the Defiant's shields were effective in this regard in 'the Search' because it utilized anti-borg technology to begin with. Fleet-wide changes didn't ensue obviously as SF has a tendency not to do that unless a threat is imminent (putting the Defiant on ice because the Borg were not an imminent threat comes to mind).
I only mentioned that it's likely the Galaxy class would not be suspended from further production because someone else mentioned they were.
I don't hold onto the premise that Galaxies were ever considered to be phased out of production.