Actually, upon further investigation it looks like we can also do overnight layovers in CDG or MAD. We have to go through DFW in any case to get to COS. Not willing to pay the BA long haul taxes and go through SEA.

The CDG Hilton is near T2, where apparently we would be arriving and departing from (AB to AA) and also has a pool.

The MAD option also has a free Hilton shuttle and the nicest pool of the bunch. Could be pleasant to get out of the cold for a bit (this trip is in March).

Focusing on Hiltons because of status and a "Be My Guest" cert to burn up.