Restricted Target Wake Time (R-TWT) is designed to prioritize latency-sensitive traffic within a Basic Service Set (BSS). However, when transmissions from Overlapping BSSs (OBSSs) overlap with the R-TWT Service Period (SP), the resulting interference may still disrupt latency sensitive traffic. The IEEE 802.11bn amendment addresses this issue by introducing Coordinated R-TWT (CR-TWT), which mandates neighboring BSSs using the same primary channel to remain silent, thereby extending SP protection. While non-overlapping R-TWT schedules guarantee protection, they may not satisfy the stringent timing requirements of delay-sensitive traffic. Conversely, allowing concurrent transmissions among Multi-Access Points (Multi-APs) in the same SP through spatial reuse can be beneficial. This poses challenges since spatial reuse typically requires a centralized coordinator to collect Received Signal Strength Indicator (RSSI) information and compute the optimal transmit power of involved APs, incurring significant signaling overhead. Meanwhile, the Traffic Identifier (TID) is critical for negotiating R-TWT SPs, as Multi-APs can utilize this information to prioritize high-priority latency-sensitive traffic. These considerations motivate our proposal of Distributed CR-TWT (DCR-TWT), which incorporates TID prioritization and formulates weighted data rate maximization as a convex optimization problem. In DCR-TWT, each AP independently solves its local optimization problem to determine whether to transmit within the SP and its corresponding optimal transmit power, greatly reducing signaling overhead. We evaluate the performance of CR-TWT and DCR-TWT using a full physical layer model coupled with a simplified Medium Access Control (MAC) layer model. An adaptive Modulation and Coding Scheme (MCS) selection mechanism is devised to enhance simulation realism. Results show that DCR-TWT outperforms CR-TWT by achieving more than two times the weighted data rate, a significant reduction in the packet error rate and the packet transmission latency. Furthermore, we identify a limitation in DCR-TWT: excessive scheduling for concurrent transmissions. This overscheduling results in up to 30% of cases failing to meet the minimum Signal-to-Interference-plus-Noise Ratio (SINR) threshold. To overcome this, we propose Enhanced DCR-TWT (EDCR-TWT), which excludes BSSs causing difficulties in the convergence of the convex optimization problem. Experimental results demonstrate a significant improvement: the proportion of cases below the minimum SINR threshold decreases from 30% to below 10% under EDCR-TWT. A comparative analysis reveals that EDCR-TWT outperforms prior work in both weighted data rate and packet error rate.