Since I was out of shape before I got even more out of shape, about the only thing I could ever have had a chance with against a ‘man at arms’ with a sword was a poleaxe. Anyone in your group using that? (Saw a bit of this on the History Channel today).
The poleaxe is a terrifying weapon, used properly. Pole arms in general have an advatange: range. Keeping thy enemy far away is pretty much always better.
There are some of the Masters that refer to the mere quarterstaff as the prince of weapons. They often waited until a student had mastered the study of longsword and all other weapons first. Showing mastery of everything else then they would demonstrate and teach to the student the quarterstaff.
Properly done, the simple staff can defeat all others.