I am a new user, but I have seen some models with bridge skew.
The xsecs do need to cross the river reach perpendicular, but I understand the xsecs shouldn’t cross your bridge/culvert/roadway. In this case, I think the remaining part of the xsec could be parallel with the center line of the bridge.
Consider this model and the 2 most downstream cross sections (highlighted). I think yours could look similar.
Does the water ever reach the low chord of the bridge? If not, you could model the piers as blocked obstructions and not worry about the skew of the bridge.