Nothing to do with downshifts, you can stop the car in neutral and it still rocks.

Still could be mounts. Maybe spark or poor fuel. Something is making your engine rock.

its difficult to determine what you mean by "The X rocks back and forth." I mean when you brake and come to a stop, does the front end dip down and then when you come to a complete stop the front end lifts back up? Because that is normal. Or when you stop does the X feel like it wants to move backward? So picture if you were coming to a stop and just before the X went to a complete stop, you let the brake go, do you thik it would roll backwards?

wow, rocking back and forth would freak me out - I'm so anal that I'm about to take my dash apart so I can stop a small rattle.

Anyway, if the back and forth you are talking about is the whole car settling when you come to a stop I would check shocks as others have stated and if your X came with air suspension I would check and make sure it is set correctly.

Do you have airsuspension?

Mine does it too. I attribute it to the crap tires that are on it. BTW I do have air susp., and just put new lower control arms on it last week.

-1 for the engine. Mine runs flawlessly, and if the OP's still does it in neutral that is the indicator that it's not engine related. Besides, it would do it continually while at a stop light.

Front to back?
Try slow sooner then easing to a stop for the last bit.
If you are coming to an abrupt stop that's like 10 tons of heavy Suv that you just stopped like a Miata. The weight lurched forward and squished the front springs. Once the momentum is gone its going back up...

I wondered the same thing -- I lose patience being a passenger in a vehicle where the driver doesn't know to slowly ease-off pressure on the brake pedal as complete stop is reached the same as you 'ease it on'. Given the weight and relative softness/compliance of the ride is this behemoth, it would certainly be worse than your average Honda and your 'peripheral vision' indicator:
your passenger pressed against the shoulder belt and then falling back again at every stop light. (Same goes for hot-rodding prior to apex on a corner: when your passenger smacks into the door? yep, you're accelerating Too Early, heheh).
No mistake - I quick-stop a Lot more than I should, the ease-off of the stop pedal nearing complete stop is just a (good) habit.. if your stealer drove it and said all is well? They don't throw away repair opportunities..
something to consider, anyway..