I'm afraid it's not possible in PulseAudio because it mixes audio streams from applications in software. It means that all streams must be converted to the same sample rate before mixing.
I guess you've already seen this: http://linux.die.net/man/5/pulse-daemon.conf
If you want quality, try setting default-sample-rate=96000. I don't think your sound card supports rates higher than 96k.
If you want speed, try resample-method=trivial, resample-method=src-sinc-fastest, resample-method=speex-float-0 and resample-method=speex-float-3, in that order. Stop when you get acceptable sound quality. (I suggest using 44,1 kHz audio for quality testing if you've set the default sample rate to 96k.)
As an alternative, try switching to ALSA. Consult your distribution's manual or wiki on how to do this. It will mix audio streams in hardware if your sound card supports this. You can check if it does by running a command:
If you see more than one line like the following:
Subdevice #0: subdevice #0
then your sound card is likely to have hardware mixing. (But I'm afraid it's not, because my laptop comes with a card similar to yours ("82801H (ICH8 Family)") and it has only one subdevice.)