Students self-assess which exercises they attempted – how can I make this more homogeneous? Background

I am organising and conducting the exercises for a graduate course.
The exercises mainly exist to give the students the opportunity to learn by doing.
However, the students also need to participate to some extent to be admitted to a final exam.
Exercises are given out as homework one week before the class.
During the class, students present their solutions to the exercises, which are discussed by other students and me.
We evaluate this as follows (which is mostly standard at my university):


At the beginning of each exercise class, a paper containing student names and the numbers of the exercises is passed around and each student checks those those tasks for which they feel that they can present a reasonable attempt to solve it.
This attempt does not need to be complete or correct; they should just be able to show what they tried and, if they failed, elaborate where they are stuck.
During the exercise class, the student presenting a given task is selected at random from those who checked it.
Tasks are so small that most of them cannot be reasonably divided into subtasks.
(This should reduce the uncertainty how to report when only half of a task was attempted.)
To be admitted to the final exam, a student has to have checked at least half of all tasks.
There is no benefit for students who have checked more exercises.


Mainly, the system seems to be working well:
I haven’t spotted an overly optimistic self-report yet and I currently expect that 0.3 students will fail the exercise criterion.

Actual Question

My biggest issue with this system is that there is a huge variation amongst students regarding how optimistic or pessimistic their self-assessment is.
In particular the system can make life more difficult for pessimistic students.
For example it happened that a student who (legitimately) checked a task and was chosen to present her attempt was stuck at some point, and another student volunteered to help out even though he did not check the task.

Hence I am asking: Is there anything I can do to effect less variability in these self-reports? In particular, I would like to flatten the pessimistic side of the spectrum.

And just because somebody is bound to remark that life is harsh and the pessimistic students need to be more optimistic anyway: Yes, but I may be able to help them learn this.
If the problem (being too pessimistic) is not too common, let the student check the exercises not only in the usual way, but also with "?".

Announce at the beginning that if students are totally unsure whether or not the may check an exercise, they may check it with "?". Then, whenever a student checked an exercise with "?", let them present this exercise (with no negative consequence whatsoever) and then say, if the attempt was resonable enough to warrant a checkmark. Announce when explaining "?", that students with "?" will have to present. (This has also the advantage that students see a not-so-perfect solution which is often more helpful and more intuitive then a perfect solution.) However, this only works if exercises do not get too often marked with "?" (as otherwise, this system could be gamed).

Some additional thoughts:


In my experience with similar systems, the "pessimistic" students are often the excellent ones, that is, the ones that pass the course anyway.
A lot of students have exactly the number of checkmarks they need to pass the course (and not more). I do think (but without proof) that if students are just at the border between passing and failing, they will do enough work to pass and get more "optimistic".
Announce in the first lesson as clearly as possible when an exercise can be checked and also, when it cannot be checked. It is often useful to give examples when it can not be checked as students may compare their situation to the example.