Grid-forming (GFM) capability requirements are increasingly imposed on grid-connected voltage-source converters (VSCs). Under large grid disturbances, GFM-VSCs need to remain stable while providing GFM services. Yet, such objectives, as pointed out in this article, inherently lead to conflicting requirements on the dynamics of the internal voltage source (IVS) of GFM-VSCs, i.e., the fast IVS dynamics is needed to avoid the loss of synchronism with the grid, whereas the slow IVS dynamics is preferred for maintaining GFM capability. To tackle this challenge, an adaptive fast/slow IVS control is proposed, which switches GFM-VSC between fast and slow IVS dynamics based on system needs. The proposed method enhances the transient stability of GFM-VSC while maximizing its capability of providing GFM service. Further, the approach is robust to different grid strengths and different types of grid disturbances. The experimental results verify the theoretical findings and the effectiveness of the proposed control method.