Multiplexed Thermocouple Considerations
If it were my design, I would use AD7708 and a separate temperature sensor on the PCB for ice point compensation.

Since 50/60Hz is a common mode signal on both TC lines, it's canceled by a differential amplifier (in the front end or in the integrated A/D).  RC filters reduce higher frequency noise, which can be rectified by the amplifier, which would cause an offset in TC reading.  Depending on the amount of noise in your environment, this may or may not be a problem.

The approach with an external mux is viable to.  Check that the mux doesn't inject too much noise.  A mechanical relay would be a really low noise mux.

edit: On floating thermocouples vs. common leads.
The topology with a common TC lead could work.  But there are caveats.  Different TCs can be a slightly different potential (common mode).  If there is a shared lead, a current may be flowing through it,  which can skew reading.  If thermocouples are spread around spatially, they may see different noise.  The noises will be added on the common lead, but will appear separately on the separate leads.  50/60Hz noise cancellation would not be as good.

update:  Related post on floating vs. grounded thermocouples.