Well, I don't know what to say to you Jack !
First, I can't find the Kv with my method, which is quite the same as Drivecalc's. Usually, with such data you can find the value of the kv by searching for which kv the calculated R increases proportionally with rpm (that's what drivecalc is looking for), using :
rpm / kv = U - RI,
R should be = a.rpm + Rm, "a" being a coefficient and "Rm" being some kind of resistance that is not influenced by rpm.
I can't find this relation with your data, the 3S and 4S values looks like being from different motors.
Then, we can guess the torque of an APC 10x4.7SF :
0.097 N.m at 5724 rpm, power out = 58 W (20°C - 30 m elevation - standard atmosphere)
0.128 N.m at 6563 rpm, power out = 88 W
estimating Io = 1.5 around 6000 rpm
( 8.77 - 1.5 ) / 0.097 = 74.6 ---> 74.6 * 30/pi = 712, this should be the kv !!,
same with 4S :
(10.69 - 1.5) / 0.128 = 71.7 ----> 71.7 * 30/pi = 685 !!
BTW, 1.9 A for no-load current at 10000 rpm is a lot IMO, I have a similar motor drawing less than the half of this.
It looks really strange ...
Maybe others have an idea...