Hi,
well, if you're sure the ~20 ohms is not a problem, then I think we can indeed stop searching for a proper switch. The big question is though: Why does it not work yet?
Well, my 20 ohm statement is based on a fixed resistor. In this case I suspect what you measured (probably with a multimeter I guess ?) might not be valid due to high non-linearity effects (see below and in the datasheet).
The nRST, CLK and I/O are still routed via the switch. The switch is in the correct position, as I can apply 3.3V with a 10kOhm resistor to any of the three lines on the 'phone' side, and I can see the corresponding signal changing on the SIM card side. However, the high-voltage is only about 2.5V on the SIM card side.
And what's the voltage on the 'phone side', (after the pullup) ? If there 0.8v voltage drop across 10k + 20 ohm, most of it must should due to the 10k ...
But now that I look at the QS3244 datasheet, the Ron is highly non-linear. At Vcc=5V and Vin=3.3V, it's even outside of the graph ... so at Vcc=3.3v you can only imagine.
Vp (Voltage pass) is speced at 4V with Vin=Vcc=5V ... so 1V drop min in that case. Here we're in a much less ideal case of Vin=Vcc=3.3V ...
I still think a bus switch is appropriate ... just not that one. (or try powering it from 5V). The SN74CB3Q3244 mentioned by Kevin seems to have much better specs at Vcc=3.3v and low voltage inputs.
Cheers,
Sylvain