I've tried this strategy a few times, but the middle seat always fills up close to departure or at the gate with NRSAs

I do echo the strategy of booking toward the back of E+. A few times I've watched the seat map progression as the gate agent clears NRSAs front to back in E+. When flying solo toward the front of E+ I've had NRSAs next to me in the middle seat while middle seats farther back in E+ left empty.