Generally speaking a higher profile tire will deliver a softer ride but there are tall sidewall tires that are also stiffer then shorter sidewalls so they may ride pretty much the same. Key with tires is to buy tires that have more flexible sidewalls if you want a better ride. Performance will be compromised with taller tires as it changes the effective gear ratio. Performance and handling are negatively impacted if the weight of the tire on the rim increases because it increases unsprung weight. It doesn't take much increase in unsprung weight to noticeably decrease acceleration and cornering capability. A softer tread rating can help ride but that usually means tires will wear faster. I wouldn't consider a non staggered setup if that is what came on the vehicle. It was fitted that way for a reason and one can only guess how to have non staggered tires to that perform as designed. Wider tires generally go on wider rims. IMO putting on tires wider than recommended for the rim is never a good idea.

If you only want to improve ride via tires then I would find a taller tire with a more flexible sidewall with a soft tire compound that weighs extremely close to the existing tires. Cornering might be negatively impacted somewhat but that doesn't seem to be your priority. That said, my solution would be to change to softer shocks and struts rather than mess with sidewall height or tire size.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas