  We construct smooth mean curvature flows with surgery that approximate
unit-regular, cylic (mod 2) Brakke flows with only spherical and neck-pinch
singularities. This is achieved by combining the recent work of
Choi-Haslhofer-Hershkovits, and Choi-Haslhofer-Hershkovits-White, establishing
canonical neighbourhoods of such singularities, with suitable barriers to flows
with surgery. A limiting argument is then used to control these approximating
flows. We conclude by improving the entropy bound on the low-entropy
Schoenflies conjecture.
