Some Cirrus CS5xxx and some from TI have built in 4:1 MUX,
AD7730 has 2:1 MUX.

Fast solution is to use 4 ADC. For math there is no difference, for fast developmet 4-chip ADC instead 4:1 muxed - is much easy. Make calculations about budget. For low low QTY there is no reason to use mux-ers.

Only 2 advantages i see in using 4 digital channels:
- a bit easy loadcell failure detection;
- possible 'numerical' calibration;
If You consider these as very valuable - go this 4D way.
Else use passive junction box and single ADC.
Or use directly IC for loadcell_to_4/20mA conversion.

Active amplifier gives nothing in Your case.
regards