This is a common problem with multiplexed ADCs. Finding a totally satisfactory solution is difficult, but I think you should start with a better opamp, something with a larger bandwidth and able to source plenty of current. I have used OP27s in the past (10 MHz GBW) for single ended applications or pre-packaged instrumentation amplifiers for differential applications (don't remember which one). The key is that the amplifier needs to have high gain at the switching frequency of the multiplexer in order to block noise from it. You have to be careful with grounding too -- ground loops and noise can ruin your day as well as noise on the signal line. I bet one of the TI fully differential opamps with ~100+ MHz bandwidth would perform pretty excellently.
Finally, don't discount passive filtering, either before or after the buffer. Filters after the buffer should be designed to avoid raising the source impedance too much, but can be very effective at blocking switching noise in the ~MHz range.