Is analog supposed to be so noisy?

It is not normal. My first thought was that you had not grounded your turntable. That seems to have been corrected or at least not been the problem. Unless of course there was a problem with the Moscode Minuet and the results just sounded the same. Unlikely but not impossible.
Try grounding the Luxman to something metal. Next check and see if the RCA jacks are as they should be. If one is very loose or not quite well connected, that could be the problem.

Did you check the cartridge connections to make sure they are secure and correctly installed? Then check the ground on your tonearm cable to make sure the ground is not broken.
To me it sounds like something in the arm is causing the problem. A broken pin or wire perhaps.

I would also check underneat the turntable to make sure the wiring is good. The last table I had like that I rewired the tonearm with better interconnect and it was a huge improvement. You also need to look at areas underneath that need lubricating. Is the grounding scheme on the TT okay? That's where I would start. I don't feel it's your preamp.

Sounds like a ground issue.

BUT

In my experience having an appliance running at the same time I'm enjoying analog, causes some hum. I live in an apartment, and whenever the fridge kicks on, or the washer/dryer is running, I'll notice some hum that is more apparent in my analog path more than digital.

This all depends on the wiring of your house of course.

Try moving your interconnects from the TT to the pre-amp and see if the hum changes. Often just passing the IC's anywhere near a power supply (including PC's) will produce a hum. Phono IC's can be a real problem sometimes!

Oh, have you located your TT near any components with power supplies, like amps? Give it lots of space from other stuff.

I'm not familar with the Luxman, but I had a TT some time ago which terminated the arm into a small box on the back of the TT and then you used your own IC's from the TT box to the pre-amp. Never wqorked w/out a hum! I replaced the box with a Cardas phono cable with a DIN plug that connected directly to the arms base and never had another problem with hum unless it was from a nearby power supply. The Cardas was not well shielded I think.

Hope this helps a bit.

My Luxman turntables have a little delicate ending to the ground wire. Consider double checking whether this wire end is actually making proper contact with the grounding post on your preamp.

Thanks, guys, for all your responses. Indeed, the ground wire was broken; I spliced it and 95% of the noise is gone. Certainly not as quiet as digital, which is practically noise-free, but quite an improvement!