For you folks with an inductance meter with four leads, (Kelvin setup), coupling factor (K) between two cores is a simple measurement; Using the well known formula, K = M/sqrt(Lp*Ls), Measure Lp and Ls the normal way but the (M) mutual inductance is measured by separating the four Kelvin leads and determining which two are the source (primary drive), normally the two outside leads on a four BNC output and the other two are the sense (secondary) leads. Drive your highest turn coupled coil with the source leads and your lower turn coupled coil by the sense leads. Read the mutual inductance directly. If the inductance reading is negative, flip one set of leads and get the same reading, only positive. The +/- sign is the phase and and easy way to determine transformer phasing. Coupling factor (K) is the same in either direction but if the low turn coil is driven and you have good coupling, you may drive the sense winding over range and not measure properly. Just though that I would mention this after seeing all the K measurement confusion.
Cheers,
Harry