The idea of introducing dedicated, fast paths between certain FPGA elements in order to reduce delay is neither new nor particularly hard to come up with. What is less obvious, however, is how to put such paths to actual use. In this work, we propose an effective ILP-based detailed placer for FPGA architectures with direct connections between LUTs. We discuss various aspects of making such an approach practicable, from efficient formulation of the integer programs themselves, to focused application of the placer on specific portions of the circuit where it could have the greatest impact. These careful considerations allow us to simultaneously move tens of LUTs with tens of candidate positions each, in a matter of minutes. This more than doubles the advantage of additional connections on the critical path delay compared to the previously reported results that relied on architecture-oblivious placement algorithms.