As a multi-hop extension of the desynchronization-based TDMA (Desync-TDMA), the extended Desync-TDMA (Ext-Desync) with self-adapting property is proposed to overcome the limitations of existing CSMA/CA and dynamic TDMA-based schemes for Mobile Ad-hoc Networks (MANETs). However, existing studies overlooked the potential problem of firing message collisions caused by node movements, leading to the severe degradation of MANET networking performance. In this paper, we derive a mathematical model to evaluate the problem due to collisions of firing messages for moving nodes. With the derived model, we propose a method for a collided node to determine whether it changes its firing phase or not, adaptively in a distributed manner, by considering both the collision situation and the slot utilization. The comparative analysis between the proposed method and existing representative ones is also presented for various networking features. The performances of the proposed method are compared with CSMA/CA as well as other existing Ext-Desync-based schemes. The numerical results show that the proposed method achieved much faster resolution and higher slot utilization in collision situations than other Ext-Desync-based schemes. In addition, we also show that the proposed method outperformed the comparable methods, including CSMA/CA, in terms of packet delivery ratios and end-to-end delays.