I wouldn't go for a big SUV unless you seriously need the space. They aren't that practical as the cargo space is not as practically used compared to a minivan and they just consume too much gas.
I think either a Lexus RX or Subaru Outback are your best choices.
The Lexus RX covers all your priorities: ride, quietness, and reliability. These are much more comfortable than the GX and close to the LX. The GX and LX ride on truck platforms so they are more bumpy. The RX rides on the Avalon car platform. Your Ridgeline rode on a car platform, not a truck platform, so expect the ride of the larger Lexus SUVs and the Expedition to have a more unsettled ride. The RX350L just debuted, but the 3rd row is practically useless. Cargo space is a little more generous in the RX350L, but there is a premium to pay.
The Subaru Outback is a nice driving car. Quiet, soft, and comfortable. The seats won't be as comfortable as the Lexus, but you aren't paying for a premium badge. Space use is very efficient and you could get a fully loaded model with over $15k to spare. It is not as reliable as the Lexus because of oil consumption, but otherwise is pretty reliable.
If you have to go with a big SUV, the 2018 Expedition is a good one. It just isn't reliable yet. Only the Toyota Sequoia and Lexus GX/LX are reliable and they don't drive well compared to the competition. The Nissan Armada is somewhat reliable but still doesn't drive well.
I can't believe no one has mentioned the Envision yet. Seems like a good fit except the cargo space.