This video might help understand where mass comes from and how to potentially modulate it, because mass can be thought of as bound energy creating voids in the gluon field:
https://m.youtube.com/watch?v=Ztc6QPNUqls
The Higgs mechanism affects electrons, not quarks, and is only responsible for about 1% of matter's mass. Most mass comes from the binding energy between quarks, which creates flux tubes between quark-antiquark pairs. If we add more energy to pull quarks apart, eventually the total energy added exceeds the mass-energy equivalence of another quark-antiquark pair, so a new pair gets created from the vacuum. I believe this is related to the Casimir effect, but IANAP (physicist).
Keep in mind that the mass-energy equivalence also applies to time. So like in the movie Interstellar, when they go down to the water planet, gravity is so high that time passes slower for them than the guy in the orbiting ship. In other words, the ship sees the landing craft move slower and slower as it approaches the surface. This difference in the speed of time near a gravity well is what slows the inner edge of a satellite slightly more than the outer, curving it along the path of the orbit, which from the satellite's perspective feels like a straight line at that velocity, because it's weightless and feels no other acceleration other than tidal force. So if someone could move large amounts of energy into a confined space with some kind of flux capacitor (is this a pun? I don't even know anymore), they could slow time there and create a virtual mass through mass-energy equivalence by E=mc^2. If they did it in front of the satellite, it would begin to increase in velocity towards that mass. So this is sort of a warp drive mechanism, although I don't know how you'd confine it, and the energies involved would be planet-scale to achieve 1 g of acceleration like near the Earth.
Also if someone made a closed loop where electron-positron pairs were sent one way, then their energy was used to create quark-antiquark pairs sent the other way, there might be a 1% imbalance in mass due to the Higgs mechanism, which would add momentum to the loop opposite the direction of the heavier stream. Although due to conservation of momentum, I suspect that this wouldn't actually happen, because any momentum above light pressure should get lost to heat/entropy/etc. But it would be a fun experiment to try. The same experiment would also work just sending light energy photons one way and matter-antimatter pairs back the other way, but I've never seen a proof as to why this would or wouldn't beat light pressure. This would be a reactionless rocket, not a warp drive.
If there's a gravity field like a gluon field, just with slightly different rules, then I don't see why it couldn't be modulated. In fact, I think that the dark matter strands connecting galaxies are densities where perhaps something like slowed neutrinos or axions collect and slow time. They could even be places where gravity "flows" along eddies left over from the Big Bang, although this seems strange to us because gravity normally only flows into gravity wells. There's also currently no explanation for the Hubble constant in the expansion of the universe, so perhaps something is creating space over time. So I don't see why space couldn't be created behind a craft to push it forward. We just don't know how.
There are so many unexplored interactions like this, that I don't think any physicist can confidently say that warp drives, reactionless rockets and folding space are impossible. Which means that I give it 50/50 odds that some kind of sci-fi space engine will be invented within the next few decades, probably starting with a reactionless drive like the EmDrive, which (if it works) uses resonance to time the interaction of microwaves with the rebound of atoms in an asymmetric field, similar to the Biefeld-Brown effect explored by Thomas Townsend Brown in the 1920s, which was later found to just be an electrohydrodynamic (EHD) effect:
https://en.wikipedia.org/wiki/Reactionless_drive
https://en.wikipedia.org/wiki/EmDrive
https://en.wikipedia.org/wiki/Biefeld–Brown_effect
Unfortunately only physicists are privy to the mental associations which allow thought experiments like this. Textbooks leave us mainly theory and equations, not insights or abstractions. Physics formulas are like trying to understand the behavior of an app from its assembly language. So in a very real way, academic gatekeeping prevented almost everyone from contributing. For every divergent thinker like Einstein, there are 100 convergent thinkers who judge skeptically and crush ideas into oblivion.
I'm just an armchair warrior full of derivative ideas who has never invented anything, who would love to run experiments like these. But just like you the reader, I'll spend the rest of my life making CRUD apps to make rent because billionaires have all the money, instead of getting to be like Dr. Gillian Taylor in Star Trek IV, suddenly able to explore every possibility under the freedom of UBI. That was a joke, but not really.