Modified digital games manage to drive motivation in repetitive exercises needed for motor rehabilitation, however designing modifications that satisfy both rehabilitation and engagement goals is challenging. We present a method wherein a statistical model of baseline gameplay identifies design configurations that emulate behaviours compatible with unmodified play. We illustrate this approach through a case study involving upper limb rehabilitation with a custom controller for a Pac-Man game. A participatory design workshop with occupational therapists defined two interaction parameters for gameplay and rehabilitation adjustments. The parameters' effect on the interaction was measured experimentally with 12 participants. We show that a low-latency model, using both user input behaviour and internal game state, identifies values for interaction parameters that reproduce baseline gameplay under degraded control. We discuss how this method can be applied to systematically balance gamification problems involving trade-offs between physical requirements and subjectively engaging experiences.