If you generate the $z$-statistics from conversion of $W$-statistics from Wilcoxon signed-rank test, that would correct for the non-normality of the data. For example, for $N_r \ge 10$, a $z$-statistic can be calculated as $z = \frac{W}{\sigma_W}, \sigma_W = \sqrt{\frac{N_r(N_r + 1)(2N_r + 1)}{6}}$. What that would then be is equivalent to a number of standard deviations of interval change of ranked data. To see whether this interval difference is significant, one converts the $z$-statistic into probability of no difference, and if the probability of no difference is small, e.g., $p<0.05$, one would accept the alternative hypothesis of a significant difference as more likely.
In other words, the above is just a description of what the Wilcoxon signed-rank test, available in most every stats package, does to calculate a probability. In Excel or R-language, this link may help.
The second part of your question relates to what was actually learned. If so, you might consider looking not at marks as percentage, but marks as 100-mark. For example, consider a student who gets a 96 on a final exam before taking the course, and a 98 (on different but similar questions) following the course. What that student did not know then went from (very approximately) 4% of the course material down to 2%, an improvement of twice (but very noisy). Similarly, a student whose mark went from 50% to 75% would have improved as much, proportionately, but still does not likely know as much of the material as the first student did before taking the course.
Summarizing, what answer you obtain depends on how you pose the question. If you want a more exact answer than the above, refine the question a bit more, and I (or someone else) may take a stab at it.
EDIT The OP has refined the question a bit. It now appears to be focused on an improvement of grades, where the information content of courses is arbitrarily assigned equal weights independent of course content, difficulty of material, knowledge of students concerning material and so forth. We still do not know what is on the tests, at least not explicitly. In a classroom environment, a typical assumption is for tests such that the first end semester test covers first semester work, and the end of second semester test covers work for both semesters. In such a case, change of grades is the only measure that is available, and improvement is measured as change in grade point average (GPA), irrespective of which courses are being taken and what the student knows, does not know, or has learned/not learned. The change of GPA can be ranked from best to worst, and the best means greatest improvement in GPA, which is a measure important to some people within the context of some school, but not very meaningful in any other context. One can take the change of GPA scores in each semester, irrespective of how many courses they represent, or what those courses are, and compare them using a one-sample Wilcoxon test, i.e., a particular student improvement compared to all improvements, and extract a one-sided probability, or a $z$ or $W$ stat from that. The probability would then have the meaning that the student's GPA from each semester (i.e., not the overall, cumulative GPA) improved significantly between semesters or not significantly compared to other, individual-semester GPA improvements. What that probability means in more general terms, is, well, not much. I would not want, on a job interview, to be known as the one who ranked first second or third for GPA improvement, or to be known as someone whose GPA improved significantly because it speaks to inconsistent performance, and poor initial performance.
IQ Scores are formulated using 100 + 15 * Z-Score
This results in a nice clean number thats easy to explain because an 80 is 'barely qualifies for elementary school' and a 120 is 'genius'
You'll still have to explain to the managers, however, why there's so little variation between good and bad scores, or why someone doesn't get a 0 for 0 contribution.
Best Answer
Welcome to the site. Of course, there are lots of ways to transform z scores into positive values: You could take absolute value, you could square them, you could add 20 to all values, you could rank them and probably some other methods. Which method should you use?
In one comment (which should be added to your question), you say:
You could certainly rank them. You would then no longer need the geometric average. But, since ranks are ordinal, you might want the median rather than the mean. That is, by ranking, you have lost some information.
For the first problem, adding a large constant could work, but I'm not at all sure geometric mean is what you want. The geometric mean is most useful when different items have different ranges - for instance, if you were trying to take the mean of GPA (range 0 to 4) and SAT scores (range 0 to 1600). z scores already do that.
If you want to value "regular good performance" then you probably need at least two numbers.