Using (and developing) haptic devices in virtual reality applications is currently impeded by the lack of flexible haptic rendering software frameworks that support haptic devices with varying numbers of interaction points. The existing open-source framework Chai3D supports primarily haptic devices with single contact points. Game engines are capable of rendering complex scenes, but typically operate at frame rates much lower than 1000 Hz, the update rate required for haptic rendering loops. We present an Unreal Engine-based extension of the UnrealHaptics framework that generalizes the prior single-contact device layer to peripherals with multiple contact points (multi-contact). The work preserves the established high-frequency haptic loop and adapts the framework to Unreal Engine 5 through a generalized device interface and component-based design. The resulting system supports heterogeneous haptic peripherals by exchanging per-contact pose data and six degrees-of-freedom force vectors. We propose a multi-contact performance benchmark and use it to validate our software architecture with two novel haptic peripherals with different numbers of contact points. Also, we propose a novel measurement method for software and hardware latencies, using audio; to quantify the effective visuo-haptic synchronicity of any software-hardware system. We show that our implementation enables fast, efficient, synchronous visuo-haptic rendering, with the haptic loop achieving a 1000 Hz update rate. Also, we demonstrate that our novel measurement method is capable of revealing the bottlenecks (here hardware) of the overall system performance. We also make our framework openly available, aiming at accelerating the development and adoption of haptic interfaces for virtual reality applications.