Less low frequencies, more upper mids.
When you say your amp gain is low, so you mean your amp has both an input gain control, and an output volume control?
One approach is to set your output volume at maximum, and use the input gain as the level control.
This way you can set the amp loud, but clean - and you learn to play with a lighter touch, so that your dynamics are preserved when you need to dig in.
If you're using a compressor of any kind (on the amp, or in pedal form), bypass it for the time being, until you've got a handle on getting the desired result from your amp.
Perhaps you have reached a point in the volume war (with too much low frequency content) that you're digging in pretty hard, and basically have nowhere left to go in terms of dynamics.
With the amps and cabs I've had, that "max the master and adjust with the gain" doesn't work at all. It is a common setting with guitarists though. There are some amps that are designed to run that way, just not the ones I use. The amps I have all have a "gain set light". The object with the gain setting is to get that gain-set (sometimes called "gain-clip" light) to dance on your lowest, loudest notes. That gives you the hottest clean sound with the lowest noise to feed to the power section.
If you turn the gain up so it always stays one, you lose some of the articulation and the clean sound it normally generates. With SS amps, distorting the preamp by running the gain too hot, pretty much never sounds good. It typically has to be designed into the preamp with either a tube in the gain for overdrive/distortion, or a tube emulating chip to dial that in. Just overdriving the gain if it's not designed for that, sounds like crap.
But that's not what you're suggesting. You're talking about running the power section all the way up all the time. And, we're not talking a 100-watt amp, which is typically the highest powered amp a guitarist uses, we're more commonly talking 500-watt to 800-watt rms amps. Running those at full level is hard on the amp and if you add a low setting on the gain, it's a noisy signal to boot because you are not sending it a strong clear signal to the power section for it to amplify.
Running a low signal into a maxed out power section gives the power section a comparatively noisy sound because the power section is generating noise itself at maximum levels and instead of producing a signal with a wide signal to noise ratio, it's just noisy. The signal to noise ratio sucks. Used to be with vinyl, if it had a 55-to-1 ration of signal to noise, that was considered high-fidelity. Anything below that isn't. You are not going to meet that threshold running the power at max and the gain low. That 55:1 ratio was from the 1970's and odds are that's not even considered high-fidelity now. Unless the amp is designed differently (READ your manual) that is not going to result in optimum sound definition, clarity or level. And running your power section at max all the time is going to generate a lot more heat and wear out internal parts at a much higher rate.
Your suggestion about playing with a light touch is spot on IMO, so you can get better dynamics - low when you want it and growling loud when you want it, based on how hard your strike the strings.
Judicious use of a compressor can also help, but don't use it if you don't need to. When you start using a compressor you are trading peak levels in the music for sustain on the notes. The compressor will compress the peaks in the music so they are not as loud and give you sustain in exchange for them. When you look at compressor ratios, 4:1 up to about 8:1 are pretty common. 4 to 1 means that you have to generate 4db higher input to get 1db in output. 8:1 means you have to generate 8db louder playing to actually increase the out put by 1db. The higher the ration, the less dynamics you can generate because the compressor is squashing those highest peaks of the input signal and with it your ability to have louder and softer dynamics in your playing. If you turn it up high enough you can get a compressor to sound like an old Farfisa Organ with no attack on the notes, no dynamics at all - all notes play at the same level - and unending sustain.
Judicious use of a compressor can be a big help though because if you adjust it correctly, you'll be limiting the peaks in the signal but it will allow you to turn up some to bring the rest of the signal closer to where your peaks were, which gives you an overall louder sound. Just be aware you will reach a point of diminishing returns with a compressor.
I have an Eden TN-226 (225-watts rms into 4Ω). I bought it specifically to play a small brewpub where we played over 40 Friday nights per year. I run it into an Eden EX-112 cab and it's perfect for this small venue as well as being easy to load in and out. I'm playing with a 5-pc group and one night we got so loud, I saw my power clipping light flashing. When that flashes, you have to fix the problem quickly or it will go into protect mode and shut off the amp. Tried turning down the Bass EQ because those low notes suck so much power - didn't work. Turned down the master until the clip light went off - couldn't be heard.
Finally engaged the auto-compressor and turned up the gain. With the compressor engaged, that gain control becomes a threshold control on that Eden amp (flashes when the compressor engages) and the higher you turn it the sooner it clamps and higher the ratio. I didn't turn the gain up that much because the gain light still flashed instead of being constantly on, but that power-clipping light went right off and I still had good dynamics. It ended up just clipping the peaks in the signal enough to keep the power section from clipping. It was smooth and very musical and a good surprise because the auto-compressor on my Eden WT amp is harsh and hard - good for slap but that's about it. You wouldn't have known I was running a compressor with this one.
So judicious use of the compressor in my situation allowed me to play at a higher SPL than I could with it off and it still sounded good. So it can be a real help if you need it. If you don't need it, don't use it is the best choice. But if you need it, use it judiciously so you don't lose all the dynamics in your playing. After that song was finished, I told everyone we needed to turn down because my amp was clipping and my ears were hurting. Everyone agreed we were too loud and turned back down. I then disengaged the auto-compressor and played normally for the rest of the night.