A new algorithm for feedback control of rotating, wall-stabilized kink modes in the High Beta Tokamak-Extended Pulse (HBT-EP) device maintains an accurate phase shift between the perturbation and the measured rotating mode through current control, with control power emphasizing fast rotation and phase jumps over fast amplitude changes. In HBT-EP, wall-stabilized kink modes become unstable above the ideal wall stability limit, and feedback suppression is aimed at delaying the onset of discharge disruption through reduction of the kink mode amplitude. Performance of the new feedback algorithm is tested under different experimental conditions, including variation of the plasma-wall coupling, insertion of a ferritic wall, changing mode rotation frequency over the range of 4-8 kHz using an internal biased electrode, and adjusting the feedback phase-angle to accelerate, amplify, or suppress the mode. We find the previously reported excitation of the slowly rotating mode at high feedback gain in HBT-EP is mitigated by the current control scheme. We also find good agreement between the observed and predicted changes to the mode rotation frequency and amplitude. When ferritic material is introduced, or the plasma-wall coupling becomes weaker as the walls are retracted from plasma, the feedback gain needs to be increased to achieve the same level of suppression. When mode rotation is slowed by a biased electrode, the feedback system still achieves mode suppression, and demonstrates wide bandwidth effectiveness.