In order to measure the time duration while my app is running, as well as the time that passed while my app was idle in the background, I need a reference clock that is not
Are you looking for something like this?
http://www.wand.net.nz/~smr26/wordpress/2009/01/19/monotonic-time-in-mac-os-x/
#include <mach/mach_time.h> into your source file.
#include <mach/mach_time.h>
replace any calls to clock_gettime(CLOCK_MONOTONIC, ×pec_t) with calls to mach_absolute_time().
clock_gettime(CLOCK_MONOTONIC, ×pec_t)
mach_absolute_time()