I am not familiar with the quote but it concerns the underground railroad so the “escaping party” must be slaves seeking freedom in the North. They are being pursued by slavers intent on preventing them from achieving their freedom. So, the quote tells us that the hunters were close to capturing them several times, but because there were so many slaves in the group, extra effort was made to assure their success by those helping them and those who shared the belief that they should succeed in achieving their freedom. Thus, everyone involved in the enterprise did everything in their power to make it easier for the escaping party to escape. In other words, this party became the priority of the underground railroad and its supporters. The path to freedom was made clear and communication was enhanced. The colonel was the leader of the pursuing party of slavers and he almost got them, but through the efforts of the antislavery groups, the “escaping party” was rushed to freedom. The author is making use of railroad terms as metaphors for what was called the underground railroad, but which never actually involved either trains or tracks.