What inductance does the 3 turn choke have?
I took a look at this tonight, testing the inductance of just one lead of the twisted pair, using a cheap LCR meter.
Results:
No ferrite: 2.4uH
0 turns: 3.1uH
1 turn: 5.3uH @ 721kHz
2 turns: 9.2uH @ 693kHz
3 turns: 14.9uH @ 657kHz
For fun, I got some of those cores and put one with 3 turns of ordinary solid hookup wire on the network analyzer (VNWA). Two runs, 1 to 1001 KHz and 1 to 501MHz.
In my case, it looks like it would do best at blocking FM radio with an impedance of 1085 ohms, not so well elsewhere.
There was only about 4 inches of wire not on the core, so lower inductances are to be expected.
Edit: added picture of core and fixture.