The diode-rectifier unit (DRU)-based high-voltage direct current (HVDC) transmission system offers an economical solution for offshore wind power transmission. However, this approach requires offshore wind farms to establish a strong grid voltage. To meet this requirement while fulfilling the dynamic characteristics of the DRU, this paper proposes an advanced grid-forming (GFM) control strategy for offshore wind turbines connected to DRU-HVDC. The strategy incorporates a P-U controller and a Q-$\omega$ controller based on reactive power synchronization. Furthermore, a novel virtual power-based pre-synchronization method and an adaptive virtual impedance technique are integrated into the proposed GFM control to improve system performance during wind turbine (WT) integration and low-voltage ride-through (LVRT) scenarios. The virtual power-based pre-synchronization method reduces voltage spikes during the integration of new wind turbines, while the adaptive virtual impedance technique effectively suppresses fault currents during low-voltage faults, enabling faster recovery. Simulation results validate the effectiveness of the proposed GFM control strategy, demonstrating improved start-up and LVRT performance through the pre-synchronization and adaptive virtual impedance methods.