The kagome ice state is a two dimensional critical state of algebraic spin correlations formed by the application of a moderate magnetic field along the cubic  direction of a pyrochlore spin ice. Tilts of the field away from perfect alignment allow for tuning of these algebraic correlations by variations of tilt angles, field or temperature, leading to symmetry-sustaining Kasteleyn transitions. We present a detailed experimental/theoretical study of the kagome ice Coulomb phase, which explores the fine tuning of critical correlations by applied field, temperature and crystal orientation. We observe the continuous modification of algebraic correlations with polarized neutron scattering experiments, and they are found to be well described by numerical simulations of an idealized model. We further clarify the thermodynamics of field tuned Kasteleyn transitions and demonstrate some dramatic finite size scaling properties that depend on how topological string defects wind around the system boundaries. We conclude that kagome ice is a remarkable example of a critical and topological state in a real system that may be subject to fine experimental control realizable at easily accessible temperatures and fields.