I was under the impression that Dyson sphere participants would be mainly heliostats, whose station would be kept by balancing their inward gravitational attraction against the outward pressure from reflected or decelerated solar wind.

Whenever an object would intersect the sphere, the nearest heliostats alter the angle of their mirrors/sails to drift away and make a hole. Then they drift back to close it after it passes.

There's nothing to say that they can't also have an orbital velocity component, as it takes quite a lot of delta-v to decelerate from a near-circular solar orbit, and orbital velocity can make up for lack of sail area.