Successive relaying can improve the transmission rate by allowing the source and relays to transmit messages simultaneously, but it may cause severe inter-relay interference (IRI). IRI cancellation schemes have been proposed to mitigate IRI. However, interference cancellation methods have a high risk of error propagation, resulting in a severe transmission rate loss in finite blocklength regimes. Thus, jointly decoding for successive relaying with finite-blocklength coding (FBC) remains a challenge. In this paper, we present an optimized channel-aware ordered successive relaying protocol with finite-blocklength coding (CAO-SIR-FBC), which can recover the rate loss by carefully adapting the relay transmission order and rate. We analyze the average throughput of the CAO-SIR-FBC method, based on which a closed-form expression in a high signal-to-noise regime (SNR) is presented. Average throughput analysis and simulations show that CAO-SIR-FBC outperforms conventional two-timeslot half-duplex relaying in terms of spectral efficiency.