I have no opinion on what the dealership’s advice might be. I however do know that unless OP asks them, OP won’t know what they’ll say. They may for example say “There are no solutions for this problem. But if you don’t like the ride, since you are one of our preferred MB customers, come in the office, let’s see if we can work a deal for you for another MB.”
Now you’re changing your tune . . . 
interesting 
The service writer will write a repair order that reads “Customer states the vehicle rides rough/stiff”.
The technician will road test and inspect the vehicle, the report will be “no problem found” and thank you for wasting my time.
The service writer is not going to try to sell the customer a new set of wheels and tires, that would cost more than $5,000 for a vehicle like this.
I’d think that’s exactly what they would recommend. If the OP has the larger optional wheels he might be willing to try it out. $5000 is a lot cheaper than a new car.
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The basic problem is that it’s a GLE63. Car and Driver said that one of the bad features of this SUV is the stiff ride. Good news! There is a cure: sell it.
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Well, it’s the GLE43, the AMG ‘lite’. But still rough it seems…
The difference is the drivetrain, not the suspension.
What is it w/Mercedes? They seem to have a farrago of model names & numbers. Are they afraid some customer might find two examples of the same model on their lot? 
The GLE43 AMG is the entry level of the AMG models with the next step up costing you closer to $40,000 more depending on options. At least that’s the delta between the GLE43 and GLE63 on the same dealers lot in Seattle.
You’d have to drive one back to back with other Amg’s but the harsh ride has been noted in several magazine reviews.
In checking the recommended tire sizes and pressure here
I note they specify 2.7 bars or 39 psi, or in some configurations 2.9 bars or 42 psi. I would think 49 lbs is simply too high, and it does not appear that you need a staggered pressure set up front and rear. I also think you probably want the option with the most sidewall.
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