The problem of authenticating feedback in overlay multicast applications has only recently been highlighted by the network security research community. The multicast source needs to verify all individual signatures on the acknowledgements (Acks) that it receives from the intended receivers - the funnelling of traffic causes, what we call the signed-Ack implosion problem. In this paper, we propose an efficient and scalable technique to solve this problem. First, we present a novel third-order linear feedback shift register (LFSR) sequence-based, 2-party signature scheme CLFSR-S following a well-known variant of the generalized ElGamal signature scheme. Second, we construct an efficient, single round, tree-based multisignature scheme CLFSR-MS (also the first multisignature based on LFSR sequences) using CLFSR-S. The CLFSR-MS scheme has been engineered to be the most efficient and scalable, tree-based multisignature scheme (owing to the unique construction/signature format of CLFSR-S) designed to solve the signed-Ack implosion problem in reliable, large-scale, performance sensitive multicast applications. We perform a theoretical analysis including correctness and security of CLFSR-MS and also present a performance (computation and communication costs, storage overhead) comparison of the proposed scheme with existing schemes.