What CD player/transport has the most stable mechanism?

I'll pile on too, Esoteric is the way to go.

why is it hugely important?

are you going to mount the thing in an off-road vehicle?

the real question is whether a unit can deal with mechanical shock electronically, mechanically or however so that SQ is not affected

Good question, I knew someone would ask.  It's because I like to dance when I listen to music, and when I do, the CD skips.  I also use my telescope from the roof, and you can see the every day vibration through the eyepiece.  Seems to me that isolation is something that isn't taken as seriously as it probably should be.  BTW, I live on a busy city street and you can feel it when a bus or truck drives by.

Thanks for the tip about the Esoteric line.  I was looking at that, but I hate dropping big coin on technology that's about to become obsolete.  Years ago I sold my Tandberg tape player for that very reason.  But hey, sometimes to have to pay to play.  I just wish, when you read reviews on digital equipment, they would talk more about this topic.  I find that it is largely ignored.  Thanks again!

I would assume a belt driven mechanism such as this from BMC or this from CEC would also deal with this issue?

But personally I'd invest in a Townshend Seismic platform and make the problem go away 

IMHO, i would look into some of the vintage Sony ES series from 1980 or around there. Build like tanks, most of these weight around 35,40 pounds , and the chassis is extremely well built. Plus, they sound pretty good and are fairly affordable.
Like I said, MHO.