How many protons are pumped out per pair of electrons from NADH in oxidative phosphorylation?
It seems like the mistake is in complex III. Look at this image from here:



It clearly shows the number of protons reduced in (and taken from) matrix and number of protons pumped into inter-membrane space. So the data becomes:

Complex I: 

matrix: 2H+ reduced (from NADH + H+) + 2H+ pumped out

IMS: 4H+ pumped in

Complex II: 

matrix: 2H+ reduced (from succinate)

IMS: 0H+ pumped in

Complex III: 

matrix: 2H+ pumped out (when not considering complex II, you'd count 4H+ here)

IMS: 4H+ pumped in (2 from complex II)

Complex IV: 

matrix: 2H+ reduced (to H2O, we won't consider it as you said) + 2H+ pumped out

IMS: 2H+ pumped in

TOTAL:

matrix: 10H+ subtracted/pumped out (with 2H+ to water, total 12H+)

IMS: 10H+ pumped in

This satisfies your statement that "10 protons are supposed to get pumped out during the electron cycle". I Hope this helps ;)

IMS = inter-membrane space