Payment channel networks have received widespread attention as an important means of scaling blockchains. Among them, the main factors affecting the selection of payment channel cross-blockchain routing include path distance, node fee quotation, etc. The existing work mainly conducts in-depth research on one of the above factors. A comprehensive evaluation function of node quality is defined, including multiple factors such as node fee quotation, path distance and historical reputation. We design a routing scheme for multi-factor reverse Vickrey auction (MFRA) to achieve a comprehensive selection of the quality of candidate intermediate nodes in the process of cross-blockchain payment routing. The MFRA routing scheme establishes the equivalent bidding function of candidate nodes, which is used to convert non-price attribute factors of node quality into price attributes. In the MFRA routing scheme, we introduce the based-2 exponential mechanism to achieve differential privacy for the equivalent bid price, which ensures the quotation anti-leak of participating nodes in the auction routing process. The security analysis and performance evaluation show that the MFRA routing scheme can effectively protect the quotation privacy of transaction participating nodes while reducing the node fee overhead, and realize efficient multi-hop cross-blockchain payment.