Coarse-grained overlays improve FPGA design productivity by providing fast compilation and software like programmability. Soft processor based overlays with well-defined ISAs are attractive to application developers due to their ease of use. However, these overlays have significant FPGA resource overheads. Time multiplexed (TM) CGRA-like overlays represent an interesting alternative as they are able to change their behavior on a cycle by cycle basis while the compute kernel executes. This reduces the FPGA resource needed, but at the cost of a higher initiation interval (II) and hence reduced throughput.The fully flexible routing network of current CGRA-like overlays results in high FPGA resource usage. However, many application kernels are acyclic and can be implemented using a much simpler linear feed-forward routing network. This paper examines a DSP block based TM overlay with linear interconnect where the overlay architecture takes account of the application kernels' characteristics and the underlying FPGA architecture, so as to minimize the II and the FPGA resource usage. We examine a number of architectural extensions to the DSP block based functional unit to improve the II, throughput and latency. The results show an average 70% reduction in II, with corresponding improvements in throughput and latency.