Clock skew scheduling (CSS) is an effective technique to optimize clock period of sequential designs. However, these techniques are not effective in the presence of certain design structural constraints that limit the CSS. In this paper, we present an analysis of several design structural constraints that affect the CSS and propose techniques to resolve these constraints. Furthermore, we propose a CSS FPGA architecture and a novel clock-period optimization (CPO) flow that tackles some of these constraints by exploiting the reconfigurability of FPGAs. Experimental results demonstrate that the proposed FPGA architecture with the CPO flow achieved an average performance improvement of 24.4% which was an average performance improvement of 10.7% over the CPO flow without considering the constraints.