Falsified student signatures in class attendance list
The system you're describing sounds like a bureaucratic nightmare to me (both for the students and for you; these things generally go hand in hand). I would therefore sympathize with (and turn a blind eye to) students tricking their way through it to the extent that is necessary to let them focus on the actual work. It's sad that they are getting free lessons in forgery when they ought to be learning something more wholesome, but as long as they are doing the coursework without academic dishonesty (as in, homework plagiarism), this should not count against them. A class is not a test of conscentiousness.

If you want to push your students to attend the class, there are other methods that don't involve automatic failure, such as giving mild homework hints in your lectures.

[Extended from my comment.]