Radiation-tolerant n-in-p planar pixel sensors have been under development in cooperation with Hamamatsu Photonics K.K. (HPK). This is geared towards applications in high-radiation environments, such as for the future Inner Tracker (ITk) placed in the innermost part of the ATLAS detector in the high luminosity LHC (HL-LHC) experiment. Prototypes of those sensors have been produced, irradiated, and evaluated over the last few years. In the previous studies, it was reported that significant drops in the detection efficiency were observed after irradiation, especially under bias structures. The bias structures are made up of poly-Si or Al bias rails and poly-Si bias resistors. The structure is implemented on the sensors to allow quality checks to be performed before the bump-bonding process, and to ensure that charge generated in floating pixels due to non-contacting or missing bump-bonds is dumped in a controlled way in order to avoid noise. To minimize the efficiency drop, several new pixel structures have been designed with bias rails and bias resistors relocated. Several test beams have been carried out to evaluate the drops in the detection efficiency of the new sensor structures after irradiation. Newly developed sensor modules were irradiated with proton-beams at the Cyclotron and Radio-Isotope Center (CYRIC) in Tohoku University to see the effect of sensor-bulk damage and surface charge-up. An irradiation with γ-rays was also carried out at Takasaki Advanced Radiation Research Center, with the goal of decoupling the effect of surface charge-up from that of bulk damage. Those irradiated sensors have been evaluated with particle beams at DESY and CERN. Comparison between different sensor structures confirmed significant improvements in minimizing efficiency loss under the bias structures after irradiation. The results from γ-irradiation also enabled cross-checking the results of a semiconductor technology simulation program (TCAD).