Looking for op amps alternatives for Pico-Amps pA4-00125-76

I think you are picking up AM radio interference because of the relatively high resistances you are using. High resistances make it easier for a low energy signal like a radio wave to imnpress a voltage on a circuit. I would suggest 2 remedies. One is to reduce all of your resistors by a factor of 10. Why do you need to put such a large resistor (R4) in series with your output? Another remedy is to put a small bypass capacitor across R2 to filter out the AM signal. If you reduce R2 to 10k, then a capacitor of about 200 pf should be sufficient. If you reduce R2 to 10k, then use a capacitor of about 2000 pf.

Firstly, regarding the selection of a sensor amplifier, go straight for an instrumentation amplifier such as the AD8221 (that's what I use for bridge and single sensor amplifiers like strain gauges): -

The advantage of an InAmp is that its input impedance is very high so it won't load the bridge and there is just one gain-set resistor needed.

Regarding the placement of the amplifier, it's a little bit open. I sometimes have up to 20 metres of cable between sensor and amplifier because the environment that my sensors are used in is usually well above 200 degC so there aint no decent silicon that can sit close by! In this scenario my DAQ is very close to my amplifier (inches away) and I use a single-ended connection to a single-ended ADC.

So, in practise, both circuits are used.

As for the theoretically best implementation for reducing noise I stand by my answer to your earlier question; a balanced signal does not need to be a differential signal - it only has to present a decent impedance balance to earth.