To reduce the noise, I wonder why they haven't investigated active noise cancelling like the engine mounts used by some auto makers. The computer introduces waveforms that are the inverse of the frequencies they want to reduce. Or at least added mass to panels that conduct noise, using material like Dynamat eXtreme (common in car audio).
I do think that active noise cancellation is a brilliant tool for solving many repetitive noise issues ( I explored its use in a server room, dual purpose was, if anything was 'wrong', I could hear the room get louder as the fans lost sync with the inverse waveform. )
However given the sensitive nature of the machines, I wonder if there would be any issues caused by projecting loud inverse waves into the room the machines operate, since it would be very strange if these equipment manufacturers didn't explore the active noise cancellation technology as a way to mitigate the ear splittingly loud noise they produce.
The other one is in the engine mounts, where they have a liquid inside the rubber mount that can stiffen up on command (maybe magnetorheological, maybe some other kind), and this is used to counteract the vibrations the engine would transmit to the body/chassis. This is controlled by the ECU because it knows when the engine is on a power stroke and can thus apply correction on a timing basis.
I would think the latter would be what the MRI makers would want to investigate -- they've got a huge spinning mass with components that vibrate. Much like an engine. :)
 At work, so can't post a video link, but if you look for "cover off mri" it's really scary/impressive how they work.