Why don't you try and make good use of that time in the US. For example if you can stopover in Chicago then you can see much of the city in 8 hours. There are trains running to downtown that cost $2 and you will get to see a lot of great sites for free. DFW is not that interesting but other cities could be pretty worthwhile. I look at long connections as an opportunity. Its the 4 hour ones that are the worst to me. Once you get into 5 or 6 hours it becomes an opportunity.

A long connection is probably the only reason I will have ever seen any of frankfurt. Even if limited to DFW, rent a car and see the JFK museum or the Fort Worth Stockyards.