I am having very similar things happening to me on my Xbox. I am playing an offline dynasty and in the last 2 days it has crashed 4 times while I have been playing. One time right as I finished the game, two other times when I was winning in the 4th quarter and another half way through the 3rd quarter.
I have sharing usage data turned on in my EA settings so I hope they are getting it. I have also tried to make sure I close the game down and even rebooted it twice and it is still happening. I get no error message or anything it just kicks me back out to the main Xbox homepage