The Third Generation Partnership Project (3GPP) Release 16 defines the sensing-based semi-persistent scheduling (SPS) as the resource allocation scheme for Sidelink Mode 2 in New Radio (NR)-based vehicle-to-everything (V2X) communication. A well-known issue in Mode 2 is the persistent packet collision that results from two or more vehicles repeatedly using the same resource for transmission. It may create serious safety problems when the vehicles are in a situation where only the broadcast safety beacons can assist in driving. To resolve this issue, a solution that relies on the feedback from neighboring vehicles is proposed, through which the vehicles suffering from persistent packet collisions can quickly part and select other resources. Extensive simulations show that the proposed broadcast feedback scheme reduces persistent packet collisions by an order of magnitude compared to SPS, and it is achieved without sacrificing the average packet reception ratio (PRR). Namely, it is the quality aspect (i.e., burstiness) of the packet collisions that the proposed scheme addresses rather than the quantity (i.e., total number of collision losses). By preventing extended packet loss events, the proposed scheme is expected to serve NR V2X better, which requires stringent QoS in terms of the information update delay thereby helping to reduce the chances of vehicle crashes.