Back in the days of long hair and big rack mounted gear effects, I would TRY to use a noise gate that was built into my Rocktron 300G compressor.
You have to set it up so that a minimal signal will "open the gate", and then the gate closes when you come back down to that minimum signal level.
I hated the fact the I could hear the noise kick in just by placing my hand on the guitar, but if I set the gate threshold any higher it would inhibit the beginning of light volume swells and the end of some notes where you're just holding onto the guitar as everything fades out, and it comes down naturally.
The gated "effect" can be just as annoying as just dealing with a little background noise, which is what I wound up doing by finding other ways to reduce the noise in the signal chain.
Sluckey and tubenit's approach are commonly used by commercial amp mfg's to tame high gain amps, and for the pennies it will cost for those caps,,,it's worth a try.
If there's that much gain and noise in that amp then it would behoove you to reduce it through circuit tweaks rather than cover it up with a gate.
Reducing the presence control setting or just reducing the NFB voltage will also help.
Also, I've found that out of the modern production preamp tubes that I have tried, the TAD 7025 has consistently been the quietest in high gain use. (as advertised)
Remember, you are amplifying the noise through each successive stage so if you've got hiss in V1, it's only gonna get worse as it goes through all of that wiring and the rest of your preamp tubes.
The amount of twang that your gonna lose by adding a couple caps is marginal....sluckey was just trying to warn you that there will be some tradeoff. The amount is controllable by how far you choose to go with the tweaks.