I have a 4-channel scope, 2 current clamps (to measure \$i_2\$ and \$i_3\$) as well as 2 voltage probes (to measure line voltages \$v_2-v_1\$ and \$v_3-v_1\$ according to the aforementioned formula). In the scope I can use math mode to multiply and sum readings, integrate and take the average over N (some many) cycles and get my power reading.
Would that work for a BLDC? I ask that since voltages and current flowing into a BLDC are full of harmonics (e.g. trapezoidal shape current) and a common wattmeter based on the 60 Hz would not suffice.