Growing electric vehicles (EVs) bring substantial vehicle-to-grid (V2G) potential. However, V2G sites and their connected grid nodes are stationary, but EV distributions are random. Therefore, in addition to the local V2G capability at the V2G sites, the punctual transfer V2G capability within the limited transfer duration is also a concern during grid V2G scheduling. To this end, this paper proposes an adaptive redistribution-based (AV2GR) method to evaluate and enhance required sites' punctual transfer V2G capabilities, thereby constructing corresponding punctual V2G scheduling and enhanced circles. Firstly, a transfer V2G redistribution (TV2GR) model is presented to evaluate the quantities and locations of punctual transfer EVs within scheduling circles under both base and transfer traffic states caused by routine vehicles and transfer EVs. Subsequently, an adaptive enhancement (ADE) algorithm is proposed to address time delays and capability reductions caused by transfer congestion, thus maximizing punctual transfer capabilities within enhanced circles. In particular, the base traffic matching (BTM) model effectively matches all transfer origins within the area to multiple scheduling destinations under variable traffic conditions. The transfer congestion index (TCI) adaptively reduces schedulable but late transfer EVs based on their contributions or sensitivities to transfer congestion. Finally, quantitative metrics considering actual V2G capability, scheduling timeliness, and potential exploitation level are constructed for comprehensive effectiveness analysis. Test results on a realistic traffic network show that the proposed AV2GR method with punctual V2G scheduling circles can maximize actual punctual transfer V2G capability while ensuring punctuality and fully exploiting the energy storage potential of idle EVs. Notably, with computation times not exceeding 1 min, the proposed ADE algorithm further enhances total actual transfer capability by up to over 25 % and increases the average potential exploitation level by over 12 %.