Roof truss with Odd 2x4 T-Shaped Reinforcement. Why is that there?
Those are stiffeners, as you suspected. Large roof systems require stabilization of those long members. The truss plan provides schedules for the carpenters to follow in adding them on-site. It makes transport simpler.
I don't think it would jeopardize the integrity of the truss by shifting them flush to one side of the truss member, but you'd need an engineer to give you legal approval. Just be sure to nail them at least as often as they are now with 12d nails or better.
Of course, you could always remove them and replace them as they are now after repairs have been made.