The Boolean satisfiability problem (SAT) is an NP-complete combinatorial optimization problem, where fast SAT solvers are useful for various smart society applications. Since these edge-oriented applications require time-critical control, a high speed SAT solver on FPGA is a promising approach. Here the authors propose a novel FPGA implementation of a bio-inspired stochastic local search algorithm called 'AmoebaSAT' on a Zynq board. Previous studies on FPGA-AmoebaSATs tackled relatively smaller-sized 3-SAT instances with a few hundred variables and found the solutions in several milli seconds. These implementations, however, adopted an instance-specific approach, which requires synthesis of FPGA configuration every time when the targeted instance is altered. In this paper, a slimmed version of AmoebaSAT named 'AmoebaSATslim,' which omits the most resource-consuming part of interactions among variables, is proposed. The FPGA-AmoebaSATslim enables to tackle significantly larger-sized 3-SAT instances, accepting 30,000 variables with 130, 800 clauses. It achieves up to approximately 24 times faster execution speed than the software-AmoebaSATslim implemented on a CPU of the x86 server.