In my experience - mostly at upscale/high-end properties - the restaurants will agree to make a substitution if I want something other than the breakfast that is normally included. If what I want is more expensive than the included breakfast option, they often will charge only the difference in price for a more expensive breakfast.

I would expect in-room breakfast to be an option at virtually all Park Hyatt properties, as this is the norm at most high-end hotels (even if they do not publish or advertise this benefit).

I once complained at the Grand Hyatt Tokyo because their restaurant breakfast menu at the French Kitchen did not include a full American Breakfast option. They had only continental, Japanese, and buffet breakfast listed on the menu in addition to a la carte items (presumably to cut costs by steering most guests who wanted a full American breakfast toward the buffet). On a more recent visit I was happy to see the menu had been revised to include a full American breakfast option served entirely at one's table.