The problem is most likely to be that the optimum input to the power amp is much smaller than the optimum output from the preamp.
In this statement, I mean "optimum" in terms of signal level - an optimum balance between overload if the signal level is too high, and noise if the signal level is too low. In this case, I think the signal level in the preamp is too low because you have to turn the attenuator too far down; the sensitive power amp then amplifies both signal and noise floor.
(There is a possibility that you just have a noisy preamp tube. The easy check is to see if there is equal noise in both channels, it's unlikely that two tubes will be equally bad. More reliable but more expensive and difficult is to try another pair of tubes.)
The best solution is to attenuate the preamp output to bring the operating signal levels closer to optimum, in both the preamp and the power amp. The best location for that attenuation is at the power amp input. On the Bottlehead Community page, I have a white paper on signals and noise which goes into much more detail if you are interested.
An input attenuator can be built into the power amp; it requires four resistors (two per channel). If you don't want to modify the amp, you can make an interconnect cable with the attenuator at the amplifier end. There are also in-line attenuators; be sure to get one with at least 10K impedance. The question is, how much attenuation is appropriate? To calculate that, you must know the amplifier sensitivity and the speaker sensitivity, as well as the preamp gain - clearly yours is a custom build, so it is not clear what the sensitivity might actually be. From your description I would guess that 12 to 20dB attenuation is needed - but that's a guess.
The snubber is a circuit modification that reduces buzz, a kind of sharp-sounding hum. This does not seem to be your problem - hiss is also called "tube rush" and is a different phenomenon.
This problem, while not common, still comes up reliably a few times every year on the forum here. A search will turn up several variations on the above comments. I'm sorry that we do not have detailed instructions for the various solutions, but many have done this and will help you do it too.