METARMan,
The issue (TSA's issue) is not leaving the United States, it is returning to the U.S. You should have no difficulty on any airline that allows your company international jumpseating getting over to Europe. It is my understanding of the TSA SD that the 24 hr. rule applies to cockpit travelers (this is according to the ALPA jumpseat chairman). However, gate agents, ticket agents, and security personel in Europe are not as up-to-date as we would like. The trick is to keep trying until you get what you want (i.e. a boarding pass to ANYWHERE in the U.S.). Also there are a few cargo carriers with cockpit doors that can accomodate international jumpseats. As the Jumpseat Chairman for my airline, I made a downloadable list of all airlines, their websites, and phone numbers, perhaps your jumpseat chairman/person has a similar list. I have heard some say "no problem" others have been "stuck for days". I think going well equipped [as many contingency plans as possible] is key. Good Luck.