topaz,
Good theory but obviously World Race Productions does not subscribe to it or we would not have only a minor possibility almost into the final leg. However, there is some hope. Trains from Paris-Gare de L'est reach Luxembourg in 4 hours. The departure schedule looks like this (F=Friday, S=Saturday, Su =Sunday):
0652 F
0753 SSu
1048 S
1347 FSSu
1753 FSSu
1951 FSSu
There is a cargo/charter airline with flights to NYC, Houston and Seattle butt that would not apply. Otherwise almost all flights from Luxembourg are to other large European cities.
Luxembourg has its own international airport for the trip to the U.S.