Does the time spent doing a PhD count towards research experience for job applications?
Typically, time spent as a graduate student counts at least to some degree as research / professional experience.  For example, the IEEE counts education culminating in a Ph.D. as five years of "professional practice," no matter how many more years it may have actually taken you.  Those 2.5 years of postdoc most definitely count, though, so it seems quite reasonable for you to apply.