It's common for usb-midi interfaces to run USB messages at 1000/second. Is it possible to remove the usb device that has midi? If it is the Scarlet, is it possible to disable the midi? If the Scarlet uses USB bus power, is there an option to use wall-wart power instead or vice versa, and does it make a difference?

A computer sized Faraday cage is not that difficult to build, actually.  
 
I'd recommend using copper mesh with small holes, but make sure they're not too small as to prevent sufficient air flow.

In my case with the MOTIF ES7, swapping the USB cable absolutely did eliminate the (digital hash) noise.
Never had that issue with a MOTIF XS7.

bvideo
It's common for usb-midi interfaces to run USB messages at 1000/second. Is it possible to remove the usb device that has midi? If it is the Scarlet, is it possible to disable the midi? If the Scarlet uses USB bus power, is there an option to use wall-wart power instead or vice versa, and does it make a difference?

Nice idea. This hypothesis might explain why the noise is less in REAPER when I'm not actively tracking, if it switches off the MIDI when transport isn't running. Unfortunately there doesn't appear to be a way to disable the MIDI on the Scarlett - there's nothing in its MixControl software, there's no separate entry for it in Device Manager, and it's already unchecked in my list of MIDI devices in Sonar. :(
 
(And no, the interface has a 12V PSU and won't run off just bus power sadly.)

Kylotan
(And no, the interface has a 12V PSU and won't run off just bus power sadly.)

You're best off using a dedicated power-supply (even if the unit can be bus-powered).
You often take a hit on fidelity when using phantom powered condenser mics.

I've found (recently) a lot of noise being picked up due to USB activity if various pieces of hardware are (or are not) using +4dBv or -10dBu.  I installed a new FX2000 (rackmount) and initially had its I/O set to +4dBv.  The amount of noise caused by moving my mouse was alarming.  When switched to -10dBu, it was almost completely silent.  This is in an aux send loop from the mixer, the sends & returns of which aren't categorised as being +4 or -10, but rather as having a maximum input/output level of +22dBu.