> I computed a simple “error score” that includes mistakes while giving blunders more weight: [number of mistakes] × 2*[number of blunders]

This doesn't give blunders more weight..

Multiplication is commutative and associative, so the author's formula is also the same as this one: 2*[number of mistakes] × [number of blunders]

To give more weight to blunders, you could use an exponent, which is a common trick in baseball statistics (SABRmetrics), like this: [number of mistakes] × [number of blunders ^ 1.1]

See e.g. some of the formula concepts invented by Bill James https://en.wikipedia.org/wiki/Bill_James#Innovations