Inspired by biological processes, neuromorphic computing utilizes spiking neural networks (SNNs) to perform inference tasks, offering significant efficiency gains for workloads involving sequential data. Recent advances in hardware and software have demonstrated that embedding a few bits of payload in each spike exchanged between the spiking neurons can further enhance inference accuracy. In a split computing architecture, where the SNN is divided across two separate devices, the device storing the first layers must share information about the spikes generated by the local output neurons with the other device. Consequently, the advantages of multi-level spikes must be balanced against the challenges of transmitting additional bits between the two devices. This paper addresses these challenges by investigating a wireless neuromorphic split computing architecture employing multi-level SNNs. For this system, we present the design of digital and analog modulation schemes optimized for an orthogonal frequency division multiplexing (OFDM) radio interface. Simulation and experimental results using software-defined radios provide insights into the performance gains of multi-level SNN models and the optimal payload size as a function of the quality of the connection between a transmitter and receiver.