The only relatively new paper that I have been able to track down was published in Mediterranean Archaeology and Archaeometry Vol 2, pages 111 to 125 and entitled 'The Mathematics of Pyramid Construction in Ancient Egypt'.

This paper contains quite a lot on MMP problem number 14 including a new proposition by its author, Flora Vafea, on how the ancient Egyptians may have worked out the formula, having studied the work of Gunn & Peet, Vogel, Thomas, Vetter, Gillings and others.

Vafea takes the view that the truncated pyramid in MMP is actually irregular, as did Struve the Russian editor of the papyrus, and may be regarded as a model of the corner stone of a pyramid.

The paper also considers the contribution of Heron of Alexandria who merely calculated the volume by the subtraction method and did not arrive at a formula.

It is easily accessible in full and can be accessed via 'Google Scholar'.

Mark