Cyclic redundancy check-aided tail-biting convolutional code (CRC-TBCC) is considered as a competitive candidate for ultra-reliable and low-latency communications (URLLC) in short-length transmission scenarios. This paper focuses on designing efficient list decoders for CRC-TBCC and constructing rate-compatible CRC-TBCC (RC-CRC-TBCC). To reduce decoding complexity, we introduce a serial list Viterbi algorithm (SLVA) based on sectionalized trellises (ST), referred to as ST-SLVA. Comparative analysis reveals that ST-SLVA significantly lowers the decoding complexity. We then propose to use selectively multiplicative repetition (SMR) to construct high-performance rate-compatible CRC-TBCC. The resulting family of codes, called SMR-CRC-TBCCs, can be decoded with the same ST-SLVA. In SMR-CRC-TBCC, adjacent coded bits of CRC-TBCC are treated as symbols of a given finite field for multiplicative repetition, with priority given to the repetition of CRC-related symbols. Simulation results demonstrate that SMR-CRC-TBCC delivers excellent performance across various coding rates. Particularly, it performs better than CRC-aided Polar (CA-Polar) codes, LTE-Turbo codes, and parallel concatenated convolutional-block (PCCB) codes. These results strengthen the competitiveness of CRC-TBCC for 6G short-length communications.