I agree with @Tuneslover. I own the Jot and M2U (and HD650) and there's a pretty noticeable difference. Definitely worth the extra money. Easiest way to go balanced is to reterminate the cheap, stock cable with 4-XLR and it was definitely worth my time. I love the balanced setup. Not just extra volume.
Not that it's the only thing worth considering, but I'll recommend the Jotunheim yet again. As @StanD mentions above, the DP-X1 has its own DAC. You can run your Rega into the phono input, the Onkyo into the unbalanced or balanced input, and still have another input available for a separate DAC at some point.
Well the Jot with phono is $500 and you'd be set. Or you could get the Mani and have $900+ to find an amp.Neither of those suggestions include a DAC, by the way, but you didn't ask for that at all. You could always get Jot with phono plus Mimby and you'd have one kick butt setup.
I don't own the HD800 so I don't know the synergy exactly, but I own and love the Jotunheim. You could buy that with phono stage built in and have a slick balanced (or not) setup.Alternately there's the Mani phono amp, and that's basically the extent of your options with Schiit.
If you're hearing it with no inputs, it would have nothing to do with your RCA interconnects, so don't waste money there.As far as power goes, make sure you try it without a surge protector. If you still have noise, try an outlet on a different circuit. If you still have noise, try to turn off anything/everything around it (just to rule out interference).