I believe a valid mathematical approach would to make 2 or 3 meringues of different stiffness, on the same day, from a single carton of eggs so that they are all the same age (this affects the whites). Pipe, or spoon the meringues into different sized mounds, an bake them all at the same time, on a parchment lined cookie sheet, at a temperature and baking duration of your choice. Then record the results of how done each of them are, graphing the results by time, thickness, and using temperature as a control. Then pipe equal amounts of meringue into different shapes, and bake again, using the same graphing criteria. You should then be able to determine empirical data that would allow you to create a mathematical model to predict the effect of the variables on the desired end product.
Using the graphs to create a model eliminates many of the variable concerns, and gives you fact-based data to build your mathematical model.
And now you know why my children always did well in Science Fairs. Being an Engineer helps develop critical thinking skills.
I hope this helps.
Seeeeeya; Chief Longwind fo the North