Worth checking the fine print. There are all sorts of issues such as "city pairs", but also "open skies" - but with lots of 'ifs' and 'buts'.
European Union:
When traveling to a destination serviced by a European Union airline, travelers flying on a Federal grant can fly on either a US carrier or an EU (European Union) carrieras long as they touch down in an EU country.
Note: travelers on federal funds cannot use city-pair contracts.
There are other exceptions to the Fly America Act which may be appropriate as well. A list of exception criteria may be found in the Federal Travel Regulation Guidelines – FTR sections 301-10.135-138. Please note that lower cost and personal convenience are not acceptable criteria for justifying the non-availability of a U.S. –flag air carrier.
Travelers using Department of Defense (DOD) are not permitted to take advantage of Open Sky Agreements. Travelers using DOD funds must use an American carrier, unless they qualify for an exemption as noted in FTR 301-10.135, sections (a), (d), (e), (f), and (g).
I have the same issue - and of course, the open skies will be all change sometime after 31 Jan since the agreement is US-EU. Do you get the government rate? Also check how up to date the policies are since they seem to updated every month.
With any status you can of course get the MCE seats - which does help (a bit).