Modular trapped-ion quantum computing hardware, known as Quantum Charge Coupled Devices (QCCDs) require shuttling operations in order to maintain effective all-to-all connectivity. Each module or trap can perform only one operation at a time, resulting in \textit{low intra-trap} parallelism, but there is no restriction on operations happening on independent traps, enabling \textit{high inter-trap} parallelism. Unlike their superconducting counterparts, the design space for QCCDs is relatively flexible and can be explored beyond the constraints of two-dimensional grids. In this work, we are motivated by the opportunity to explore the QCCD design space in the context of optimizing for non-topological CSS codes. In particular, current grid-based architectures significantly limit the performance of many promising, high-rate codes such as hypergraph product codes and bivariate bicycle codes. Many of these codes are highly parallelizable, meaning that with appropriate hardware layouts and matching software schedules, execution latency can be greatly reduced. Faster execution, in turn, reduces error accumulation from decoherence and heating, ultimately improving code performance when mapped to realistic hardware.

However, current 2D grid designs suffer from numerous trap to trap ``roadblocks", forcing serialization and destroying the inherent parallelism of these codes. To address this, we propose \textit{Cyclone}, a circular software-hardware codesign that departs from traditional 2D grids in favor of a flexible ring topology, where ancilla qubits move in lockstep. Cyclone eliminates roadblocks, bounds total movement, and enables high levels of parallelism, resulting in up to ~4$\times$ speedup in execution times. In addition to temporal efficiency, Cyclone also offers large spatial efficiency when compared to a grid codesign. It requires fewer traps, fewer junctions, and only a single Digital-to-Analog Converter (DAC), as opposed to grid architectures, where DAC count scales linearly with the number of traps. With hypergraph product codes, Cyclone achieves up to a 2$\times$ order of magnitude improvement in logical error rate, and with bivariate bicycle codes, this improvement reaches up to a 3$\times$ in order of magnitude. Spatially, Cyclone reduces the number of required traps and ancilla qubits by $2\times$. The overall spacetime improvement over a standard grid is up to $\sim 20 \times$, demonstrating Cyclone as a scalable and efficient alternative to conventional 2D QCCD architectures.