Just-in-time (JIT) compilation has been used in many applications to enable standard software binaries to execute on different underlying processor architectures. We previously introduced the concept of a standard hardware binary, using a just-in-time compiler to compile the hardware binary to a field-programmable gate array (FPGA). Our JIT compiler includes lean versions of technology mapping, placement, and routing algorithms, of which routing is the most computationally and memory expensive step. As FPGAs continue to increase in size, a JIT FPGA compiler must be capable of efficiently mapping increasingly larger hardware circuits. In this paper, we analyze the scalability of our lean on-chip router, the Riverside On-Chip Router (ROCR), for routing increasingly large hardware circuits. We demonstrate that ROCR scales well in terms of execution time, memory usage and circuit quality, and we compare the scalability of ROCR to the well known Versatile Place and Route (VPR) timing-driven routing algorithm, comparing to both their standard routing algorithm and their fast routing algorithm. Our results show that on average ROCR executes 3 times faster using 18 times less memory than VPR. ROCR requires only 1% more routing resources, while creating a critical path 30% longer VPR's standard timing-driven router. Furthermore, for the largest hardware circuit, ROCR executes 3 times faster using 14 times less memory, and results in a critical path 2.6% shorter than VPR's fast timing-driven router.