I think the construction method or material of the chassis is irrelevant. i think the road race guys use square because the rules allow it and it is easier to construct.
High end drag cars use round due to NHRA requirements. and weight.
The key is in the suspension and a drag race 4 link will never work in a corner.
the road race stuff likely would cross over better to the drag strip as they still want traction but will never be as good as a 4 link.
I don't think there is a happy medium. i think you can have huge compromises in both to get to the middle but would not be happy at either event.
the simple answer is to just build 2 cars!!