Congrats on your new DAC Gene, nice choice. Since the DAC plays music OK, then the opamps were installed correctly.
The tube should not cause any trouble, but pull it just to remove the variable. Once you find the quiet then you can start adding things back.
If this is EE DAC version 1 with volume control, connect the DAC directly to the amp. If it is version 2 use Duet to turn down the volume digitally, then connect to amp. By removing the preamp, if the hum is gone you exonerate the DAC and amp.
Hum is usually caused by resistance in the ground circuit. Ground is not absolute zero volts. Silent ground need only be the same ground voltage everywhere, but not necessarily zero volts. Resistance on ground connections causes voltage to vary in the ground circuit, causing current to flow and make the hum. Your mission, if you choose to accept it, is to find the source of resistance.
Most components do connect the signal and chassis grounds together inside the component, so that's how loops form between signal and power sides, they are both part of the ground circuit. The total ground circuit includes the whole system and the house wiring, not just the grounding inside one component. Their grounds all connect together so it is one big circuit. There is always voltage on a ground circuit, but if it's the same everywhere then it's silent. A few mV is common. But if there is any abnormally high resistance anywhere in the ground circuit then current will flow across that resistance and this current is the hum. It hums like AC because AC power supply is always grounded for safety. But even battery powered components can be a source of hum when connected by IC to an AC powered component.
Clean tight wires is first thing to check. Usually the resistance comes from temporary connections. These can be obvious, like dirty RCA plugs and jacks, or hidden, like two outlets with separate grounds. One outlet ground runs back to service box with dedicated ground wire. The other outlet is a shared circuit with wire stabbed outlets and a ceiling lamp with twisted connections. All those mechanical connections increase resistance, causing a ground loop in the house wiring when those two outlets are used simultaneously in a audio system that is interconnected with signal wires. Moving your ground testing system to one outlet cures this.
Any kind of antenna, cable or satellite cables will usually cause hum. Also think of whatever other changes may have happened in addition to the new DAC. Moving things around, changing plugs, etc. Often several changes are made at the same time that we don't realize. Simplifying the system to basic components removes those variables.