Update:
The noise I was hearing only happened when the temp was below about 30F, and seemed to get worse as the temp dropped. It sounded a little like tapping on something solid (like a windshield or a table) with a key. Definately a tap, not a squeak as I would have expected with a suspension part. I picked it up yesterday afternoon after they replaced the "shock tops". I have no idea what those are, but it sounds like my previous understanding (based on their original description) might have been wrong. I haven't looked to see if I can see anything different.
Apparently, the issue I was having might be unique to the FSport, but that would surprise me a little. I thought the only difference in the FSport was the shocks, and mine has the lowering springs, but the issue wasn't with either of these parts. They said the part they replaced has been redesigned, which tells me they are aware of the issue even though it might be a little uncommon.
In any event, I got to drive their RX450h around for a week on their gas, and the noise was missing when I drove it home in 14 degree weather.