We formulate the complete C1 boundary-value matching problem for non-singular anisotropic matter interiors that can excise the naked ring singularity and the compact closed-timelike-curve torus of the hyperextreme Kerr vortex. Paper 1 showed that a hollow Z2 mirror shell requires negative surface energy density. Here we drop mirror symmetry and write the full asymmetric Israel junction conditions across a toroidal surface Στ0 (physical tube radius ϵ = 2a e−τ0 ), including all diagonal and off-diagonal extrinsic-curvature components. Seamless C1 matching (Sa b = 0) holds if and only if the interior radial derivatives of the three metric potentials coincide with those of the exterior Kerr solution on Στ0. Core regularity is analysed in a regular polar disk chart covering the focal ring; quadratic decay of the potentials guarantees that the Kretschmann scalar and the fluid density remain finite. We derive the stationary axisymmetric Einstein–fluid equations and the resulting differential inequalities that any Weak-Energy-Condition-satisfying interior must obey. We restrict the excision to the static-limit-admissible region f0(σ) > 0, prove that the WEC energy density ρm > 0 is attainable at leading order in a boundary layer by free choice of the second-order profiles (so the solution space is non-empty), and establish the exact algebraic condition f2− ω2− < ρ2 under which the matter core itself remains free of closed timelike curves. Full simultaneous satisfaction of all WEC inequalities across a finite layer with a fixed constitutive model remains an open free-boundary problem.