The Trails exercise was designed for a fully virtual course, but it is applicable in any course where discussion is online. I am less sure how useful this will be for real-time discussion. Here are some ideas for ways in which the exercise might be altered.

The topics might be chosen according to different principles. Instead of being topics not covered by lecture, they could be extensions to it, covering material not designed into the lecture material itself. If you put your lecture notes online, then the Trails page could be appended directly to that (for example, adding links to the Wars of the Roses on to the end of a lecture on the Hundred Years War). Or you could place a link at appropriate places in the class schedule, so that the encounter was at specific times across the semester.

The reporting could be more formal. It might be appropriate to require the initial report to follow certain standards or adhere to a certain form, which follow-up discussion being allowed to remain informal. This still would not need to be graded, but a few points might be assigned based on whether the form had been followed or not.The questions themselves could be made more formal, with specific responses expected.

The students could work in teams. This would be a way to handle a larger class size. It would also be a way to know exactly what each student in the team contributed to the whole. Here, too, the assignment could be made more formal or more structured, with specific task assignments within the team.

At a certain point, the exercise begins to become something else. If it were made a requirement, if deadlines were imposed, if it were graded separately, then it moves beyond its current role and the dynamics and benefits would also change. There's nothing wrong with doing this, but the exercise would no longer be addressing the original issue of how to get students to read material that is optional.