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The tilt and shift stability of a spheromak plasma in the presence of a large orbit ion-ring component is determined by evaluating the magnetic interaction of the plasma with the ion ring and the external coils. Neither the ion-ring toroidal current nor the ring inverse aspect ratio is required to be small. The influence of conducting walls is considered to be negligible, as is appropriate for compression experiments. The plasma tilt and shift stability has been evaluated for a comprehensive set of numerically generated, self-consistent, hybrid spheromak/ion-ring equilibria. Stable equilibria are found over a considerable range of the parameters. The tilt stabilization of the plasma typically requires that more than about 25% of the total toroidal current be carried by the ion ring.